Hilbert bundles with ends Article Swipe
Tsuyoshi Kato
,
Daisuke Kishimoto
,
Mitsunobu Tsutaya
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1142/s1793525321500680
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1142/s1793525321500680
Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and different from an end as a metric space. Such an indexed basis also defines unitary operators of finite propagation, and these operators preserve an end of a Hilbert space. Then, we can define a Hilbert bundle with end, which lightens up new structures of Hilbert bundles. In a special case, we can define characteristic classes of Hilbert bundles with ends, which are new invariants of Hilbert bundles. We show Hilbert bundles with ends appear in natural contexts. First, we generalize the pushforward of a vector bundle along a finite covering to an infinite covering, which is a Hilbert bundle with end under a mild condition. Then we compute characteristic classes of some pushforwards along infinite coverings. Next, we will show the spectral decompositions of nice differential operators give rise to Hilbert bundles with ends, which elucidate new features of spectral decompositions. The spectral decompositions we will consider are the Fourier transform and the harmonic oscillators.
Related Topics
Concepts
Mathematics
Hilbert space
Pure mathematics
Hilbert manifold
Rigged Hilbert space
Vector bundle
Hilbert R-tree
Hilbert series and Hilbert polynomial
Reproducing kernel Hilbert space
Countable set
Fiber bundle
Metric (unit)
Projective Hilbert space
Hilbert–Poincaré series
Mathematical analysis
Bundle
Operations management
Materials science
Economics
Composite material
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1142/s1793525321500680
- OA Status
- green
- References
- 11
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3160721277
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W3160721277Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1142/s1793525321500680Digital Object Identifier
- Title
-
Hilbert bundles with endsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-12-31Full publication date if available
- Authors
-
Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu TsutayaList of authors in order
- Landing page
-
https://doi.org/10.1142/s1793525321500680Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2105.02981Direct OA link when available
- Concepts
-
Mathematics, Hilbert space, Pure mathematics, Hilbert manifold, Rigged Hilbert space, Vector bundle, Hilbert R-tree, Hilbert series and Hilbert polynomial, Reproducing kernel Hilbert space, Countable set, Fiber bundle, Metric (unit), Projective Hilbert space, Hilbert–Poincaré series, Mathematical analysis, Bundle, Operations management, Materials science, Economics, Composite materialTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
11Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W3160721277 |
|---|---|
| doi | https://doi.org/10.1142/s1793525321500680 |
| ids.doi | https://doi.org/10.48550/arxiv.2105.02981 |
| ids.mag | 3160721277 |
| ids.openalex | https://openalex.org/W3160721277 |
| fwci | |
| type | preprint |
| title | Hilbert bundles with ends |
| biblio.issue | 02 |
| biblio.volume | 16 |
| biblio.last_page | 322 |
| biblio.first_page | 291 |
| topics[0].id | https://openalex.org/T11304 |
| topics[0].field.id | https://openalex.org/fields/27 |
| topics[0].field.display_name | Medicine |
| topics[0].score | 0.8955000042915344 |
| topics[0].domain.id | https://openalex.org/domains/4 |
| topics[0].domain.display_name | Health Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2741 |
| topics[0].subfield.display_name | Radiology, Nuclear Medicine and Imaging |
| topics[0].display_name | Advanced Neuroimaging Techniques and Applications |
| topics[1].id | https://openalex.org/T10896 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.8291000127792358 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2610 |
| topics[1].subfield.display_name | Mathematical Physics |
| topics[1].display_name | Homotopy and Cohomology in Algebraic Topology |
| topics[2].id | https://openalex.org/T12622 |
| topics[2].field.id | https://openalex.org/fields/27 |
| topics[2].field.display_name | Medicine |
| topics[2].score | 0.796999990940094 |
| topics[2].domain.id | https://openalex.org/domains/4 |
| topics[2].domain.display_name | Health Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2728 |
| topics[2].subfield.display_name | Neurology |
| topics[2].display_name | Neurosurgical Procedures and Complications |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C33923547 |
| concepts[0].level | 0 |
| concepts[0].score | 0.7502292394638062 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[0].display_name | Mathematics |
| concepts[1].id | https://openalex.org/C62799726 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6271750926971436 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q190056 |
| concepts[1].display_name | Hilbert space |
| concepts[2].id | https://openalex.org/C202444582 |
| concepts[2].level | 1 |
| concepts[2].score | 0.5834833383560181 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[2].display_name | Pure mathematics |
| concepts[3].id | https://openalex.org/C147493315 |
| concepts[3].level | 3 |
| concepts[3].score | 0.5802273154258728 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q3554824 |
| concepts[3].display_name | Hilbert manifold |
| concepts[4].id | https://openalex.org/C60064506 |
| concepts[4].level | 4 |
| concepts[4].score | 0.5581021308898926 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q1262627 |
| concepts[4].display_name | Rigged Hilbert space |
| concepts[5].id | https://openalex.org/C95857938 |
| concepts[5].level | 2 |
| concepts[5].score | 0.5267379283905029 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q658429 |
| concepts[5].display_name | Vector bundle |
| concepts[6].id | https://openalex.org/C76103427 |
| concepts[6].level | 5 |
| concepts[6].score | 0.5175530314445496 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q5761197 |
| concepts[6].display_name | Hilbert R-tree |
| concepts[7].id | https://openalex.org/C57033185 |
| concepts[7].level | 3 |
| concepts[7].score | 0.48923230171203613 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q5761236 |
| concepts[7].display_name | Hilbert series and Hilbert polynomial |
| concepts[8].id | https://openalex.org/C80884492 |
| concepts[8].level | 3 |
| concepts[8].score | 0.4409205913543701 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q3345678 |
| concepts[8].display_name | Reproducing kernel Hilbert space |
| concepts[9].id | https://openalex.org/C110729354 |
| concepts[9].level | 2 |
| concepts[9].score | 0.4301784634590149 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q185478 |
| concepts[9].display_name | Countable set |
| concepts[10].id | https://openalex.org/C146710177 |
| concepts[10].level | 3 |
| concepts[10].score | 0.4296847879886627 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q1154996 |
| concepts[10].display_name | Fiber bundle |
| concepts[11].id | https://openalex.org/C176217482 |
| concepts[11].level | 2 |
| concepts[11].score | 0.4274793565273285 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q860554 |
| concepts[11].display_name | Metric (unit) |
| concepts[12].id | https://openalex.org/C36185835 |
| concepts[12].level | 4 |
| concepts[12].score | 0.42089059948921204 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q3058230 |
| concepts[12].display_name | Projective Hilbert space |
| concepts[13].id | https://openalex.org/C185982889 |
| concepts[13].level | 2 |
| concepts[13].score | 0.4165623188018799 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q5761255 |
| concepts[13].display_name | Hilbert–Poincaré series |
| concepts[14].id | https://openalex.org/C134306372 |
| concepts[14].level | 1 |
| concepts[14].score | 0.3743842840194702 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[14].display_name | Mathematical analysis |
| concepts[15].id | https://openalex.org/C2778134712 |
| concepts[15].level | 2 |
| concepts[15].score | 0.3649081587791443 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q1047307 |
| concepts[15].display_name | Bundle |
| concepts[16].id | https://openalex.org/C21547014 |
| concepts[16].level | 1 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q1423657 |
| concepts[16].display_name | Operations management |
| concepts[17].id | https://openalex.org/C192562407 |
| concepts[17].level | 0 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[17].display_name | Materials science |
| concepts[18].id | https://openalex.org/C162324750 |
| concepts[18].level | 0 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q8134 |
| concepts[18].display_name | Economics |
| concepts[19].id | https://openalex.org/C159985019 |
| concepts[19].level | 1 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q181790 |
| concepts[19].display_name | Composite material |
| keywords[0].id | https://openalex.org/keywords/mathematics |
| keywords[0].score | 0.7502292394638062 |
| keywords[0].display_name | Mathematics |
| keywords[1].id | https://openalex.org/keywords/hilbert-space |
| keywords[1].score | 0.6271750926971436 |
| keywords[1].display_name | Hilbert space |
| keywords[2].id | https://openalex.org/keywords/pure-mathematics |
| keywords[2].score | 0.5834833383560181 |
| keywords[2].display_name | Pure mathematics |
| keywords[3].id | https://openalex.org/keywords/hilbert-manifold |
| keywords[3].score | 0.5802273154258728 |
| keywords[3].display_name | Hilbert manifold |
| keywords[4].id | https://openalex.org/keywords/rigged-hilbert-space |
| keywords[4].score | 0.5581021308898926 |
| keywords[4].display_name | Rigged Hilbert space |
| keywords[5].id | https://openalex.org/keywords/vector-bundle |
| keywords[5].score | 0.5267379283905029 |
| keywords[5].display_name | Vector bundle |
| keywords[6].id | https://openalex.org/keywords/hilbert-r-tree |
| keywords[6].score | 0.5175530314445496 |
| keywords[6].display_name | Hilbert R-tree |
| keywords[7].id | https://openalex.org/keywords/hilbert-series-and-hilbert-polynomial |
| keywords[7].score | 0.48923230171203613 |
| keywords[7].display_name | Hilbert series and Hilbert polynomial |
| keywords[8].id | https://openalex.org/keywords/reproducing-kernel-hilbert-space |
| keywords[8].score | 0.4409205913543701 |
| keywords[8].display_name | Reproducing kernel Hilbert space |
| keywords[9].id | https://openalex.org/keywords/countable-set |
| keywords[9].score | 0.4301784634590149 |
| keywords[9].display_name | Countable set |
| keywords[10].id | https://openalex.org/keywords/fiber-bundle |
| keywords[10].score | 0.4296847879886627 |
| keywords[10].display_name | Fiber bundle |
| keywords[11].id | https://openalex.org/keywords/metric |
| keywords[11].score | 0.4274793565273285 |
| keywords[11].display_name | Metric (unit) |
| keywords[12].id | https://openalex.org/keywords/projective-hilbert-space |
| keywords[12].score | 0.42089059948921204 |
| keywords[12].display_name | Projective Hilbert space |
| keywords[13].id | https://openalex.org/keywords/hilbert–poincaré-series |
| keywords[13].score | 0.4165623188018799 |
| keywords[13].display_name | Hilbert–Poincaré series |
| keywords[14].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[14].score | 0.3743842840194702 |
| keywords[14].display_name | Mathematical analysis |
| keywords[15].id | https://openalex.org/keywords/bundle |
| keywords[15].score | 0.3649081587791443 |
| keywords[15].display_name | Bundle |
| language | en |
| locations[0].id | doi:10.1142/s1793525321500680 |
| locations[0].is_oa | False |
| locations[0].source.id | https://openalex.org/S167996400 |
| locations[0].source.issn | 1793-5253, 1793-7167 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 1793-5253 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Journal of Topology and Analysis |
| locations[0].source.host_organization | https://openalex.org/P4310319815 |
| locations[0].source.host_organization_name | World Scientific |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310319815 |
| locations[0].license | |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Journal of Topology and Analysis |
| locations[0].landing_page_url | https://doi.org/10.1142/s1793525321500680 |
| locations[1].id | pmh:oai:arXiv.org:2105.02981 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | |
| locations[1].pdf_url | https://arxiv.org/pdf/2105.02981 |
| locations[1].version | submittedVersion |
| locations[1].raw_type | text |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | http://arxiv.org/abs/2105.02981 |
| locations[2].id | mag:3160721277 |
| locations[2].is_oa | True |
| locations[2].source.id | https://openalex.org/S4306400194 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | True |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | arXiv (Cornell University) |
| locations[2].source.host_organization | https://openalex.org/I205783295 |
| locations[2].source.host_organization_name | Cornell University |
| locations[2].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[2].license | |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | |
| locations[2].license_id | |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | arXiv (Cornell University) |
| locations[2].landing_page_url | https://arxiv.org/pdf/2105.02981 |
| locations[3].id | doi:10.48550/arxiv.2105.02981 |
| locations[3].is_oa | True |
| locations[3].source.id | https://openalex.org/S4306400194 |
| locations[3].source.issn | |
| locations[3].source.type | repository |
| locations[3].source.is_oa | True |
| locations[3].source.issn_l | |
| locations[3].source.is_core | False |
| locations[3].source.is_in_doaj | False |
| locations[3].source.display_name | arXiv (Cornell University) |
| locations[3].source.host_organization | https://openalex.org/I205783295 |
| locations[3].source.host_organization_name | Cornell University |
| locations[3].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[3].license | cc-by |
| locations[3].pdf_url | |
| locations[3].version | |
| locations[3].raw_type | article |
| locations[3].license_id | https://openalex.org/licenses/cc-by |
| locations[3].is_accepted | False |
| locations[3].is_published | |
| locations[3].raw_source_name | |
| locations[3].landing_page_url | https://doi.org/10.48550/arxiv.2105.02981 |
| indexed_in | arxiv, crossref, datacite |
| authorships[0].author.id | https://openalex.org/A5031832499 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-5311-4966 |
| authorships[0].author.display_name | Tsuyoshi Kato |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Tsuyoshi Kato |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5078587619 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-7837-8818 |
| authorships[1].author.display_name | Daisuke Kishimoto |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Daisuke Kishimoto |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5051870042 |
| authorships[2].author.orcid | https://orcid.org/0000-0003-1834-893X |
| authorships[2].author.display_name | Mitsunobu Tsutaya |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Mitsunobu Tsutaya |
| authorships[2].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2105.02981 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Hilbert bundles with ends |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11304 |
| primary_topic.field.id | https://openalex.org/fields/27 |
| primary_topic.field.display_name | Medicine |
| primary_topic.score | 0.8955000042915344 |
| primary_topic.domain.id | https://openalex.org/domains/4 |
| primary_topic.domain.display_name | Health Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2741 |
| primary_topic.subfield.display_name | Radiology, Nuclear Medicine and Imaging |
| primary_topic.display_name | Advanced Neuroimaging Techniques and Applications |
| related_works | https://openalex.org/W1874570008, https://openalex.org/W97912353, https://openalex.org/W2187412439, https://openalex.org/W2129693403, https://openalex.org/W111924430, https://openalex.org/W1886250216, https://openalex.org/W2752222682, https://openalex.org/W2046178815, https://openalex.org/W1514746830, https://openalex.org/W3098129592, https://openalex.org/W3120653109, https://openalex.org/W1725763662, https://openalex.org/W292412354, https://openalex.org/W2182923757, https://openalex.org/W2246998535, https://openalex.org/W2951442461, https://openalex.org/W2040164829, https://openalex.org/W2345560347, https://openalex.org/W3202015171, https://openalex.org/W2527137842 |
| cited_by_count | 0 |
| locations_count | 4 |
| best_oa_location.id | pmh:oai:arXiv.org:2105.02981 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2105.02981 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2105.02981 |
| primary_location.id | doi:10.1142/s1793525321500680 |
| primary_location.is_oa | False |
| primary_location.source.id | https://openalex.org/S167996400 |
| primary_location.source.issn | 1793-5253, 1793-7167 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 1793-5253 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Journal of Topology and Analysis |
| primary_location.source.host_organization | https://openalex.org/P4310319815 |
| primary_location.source.host_organization_name | World Scientific |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319815 |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Journal of Topology and Analysis |
| primary_location.landing_page_url | https://doi.org/10.1142/s1793525321500680 |
| publication_date | 2021-12-31 |
| publication_year | 2021 |
| referenced_works | https://openalex.org/W1570658674, https://openalex.org/W2023944555, https://openalex.org/W2060516091, https://openalex.org/W2327652045, https://openalex.org/W2012949987, https://openalex.org/W4213082596, https://openalex.org/W1987708986, https://openalex.org/W2003445593, https://openalex.org/W2112188251, https://openalex.org/W3099265680, https://openalex.org/W3042328344 |
| referenced_works_count | 11 |
| abstract_inverted_index.a | 1, 11, 14, 31, 40, 61, 68, 82, 118, 122, 131, 137 |
| abstract_inverted_index.In | 81 |
| abstract_inverted_index.We | 102 |
| abstract_inverted_index.an | 23, 37, 44, 58, 126 |
| abstract_inverted_index.as | 39 |
| abstract_inverted_index.by | 18 |
| abstract_inverted_index.in | 109 |
| abstract_inverted_index.is | 30, 130 |
| abstract_inverted_index.of | 13, 25, 51, 60, 78, 90, 99, 117, 145, 158, 173 |
| abstract_inverted_index.to | 125, 164 |
| abstract_inverted_index.up | 75 |
| abstract_inverted_index.we | 5, 65, 85, 113, 141, 152, 179 |
| abstract_inverted_index.The | 176 |
| abstract_inverted_index.and | 34, 54, 186 |
| abstract_inverted_index.are | 96, 182 |
| abstract_inverted_index.can | 6, 66, 86 |
| abstract_inverted_index.end | 24, 38, 59, 135 |
| abstract_inverted_index.its | 8 |
| abstract_inverted_index.new | 32, 76, 97, 171 |
| abstract_inverted_index.the | 19, 26, 115, 155, 183, 187 |
| abstract_inverted_index.Such | 43 |
| abstract_inverted_index.Then | 10, 140 |
| abstract_inverted_index.also | 47 |
| abstract_inverted_index.end, | 72 |
| abstract_inverted_index.end. | 9 |
| abstract_inverted_index.ends | 107 |
| abstract_inverted_index.from | 36 |
| abstract_inverted_index.give | 162 |
| abstract_inverted_index.mild | 138 |
| abstract_inverted_index.nice | 159 |
| abstract_inverted_index.rise | 163 |
| abstract_inverted_index.show | 103, 154 |
| abstract_inverted_index.some | 146 |
| abstract_inverted_index.will | 153, 180 |
| abstract_inverted_index.with | 71, 93, 106, 134, 167 |
| abstract_inverted_index.Given | 0 |
| abstract_inverted_index.Next, | 151 |
| abstract_inverted_index.Then, | 64 |
| abstract_inverted_index.along | 121, 148 |
| abstract_inverted_index.basis | 12, 46 |
| abstract_inverted_index.case, | 84 |
| abstract_inverted_index.ends, | 94, 168 |
| abstract_inverted_index.space | 16, 21 |
| abstract_inverted_index.these | 55 |
| abstract_inverted_index.under | 136 |
| abstract_inverted_index.which | 29, 73, 95, 129, 169 |
| abstract_inverted_index.First, | 112 |
| abstract_inverted_index.appear | 108 |
| abstract_inverted_index.bundle | 70, 120, 133 |
| abstract_inverted_index.define | 67, 87 |
| abstract_inverted_index.finite | 52, 123 |
| abstract_inverted_index.metric | 3, 20, 41 |
| abstract_inverted_index.notion | 33 |
| abstract_inverted_index.space, | 4, 28 |
| abstract_inverted_index.space. | 42, 63 |
| abstract_inverted_index.vector | 119 |
| abstract_inverted_index.Fourier | 184 |
| abstract_inverted_index.Hilbert | 15, 27, 62, 69, 79, 91, 100, 104, 132, 165 |
| abstract_inverted_index.bundles | 92, 105, 166 |
| abstract_inverted_index.classes | 89, 144 |
| abstract_inverted_index.compute | 142 |
| abstract_inverted_index.defines | 22, 48 |
| abstract_inverted_index.indexed | 17, 45 |
| abstract_inverted_index.natural | 110 |
| abstract_inverted_index.special | 83 |
| abstract_inverted_index.unitary | 49 |
| abstract_inverted_index.bundles. | 80, 101 |
| abstract_inverted_index.consider | 7, 181 |
| abstract_inverted_index.covering | 124 |
| abstract_inverted_index.features | 172 |
| abstract_inverted_index.harmonic | 188 |
| abstract_inverted_index.infinite | 127, 149 |
| abstract_inverted_index.lightens | 74 |
| abstract_inverted_index.preserve | 57 |
| abstract_inverted_index.spectral | 156, 174, 177 |
| abstract_inverted_index.contexts. | 111 |
| abstract_inverted_index.countable | 2 |
| abstract_inverted_index.covering, | 128 |
| abstract_inverted_index.different | 35 |
| abstract_inverted_index.elucidate | 170 |
| abstract_inverted_index.operators | 50, 56, 161 |
| abstract_inverted_index.transform | 185 |
| abstract_inverted_index.condition. | 139 |
| abstract_inverted_index.coverings. | 150 |
| abstract_inverted_index.generalize | 114 |
| abstract_inverted_index.invariants | 98 |
| abstract_inverted_index.structures | 77 |
| abstract_inverted_index.pushforward | 116 |
| abstract_inverted_index.differential | 160 |
| abstract_inverted_index.oscillators. | 189 |
| abstract_inverted_index.propagation, | 53 |
| abstract_inverted_index.pushforwards | 147 |
| abstract_inverted_index.characteristic | 88, 143 |
| abstract_inverted_index.decompositions | 157, 178 |
| abstract_inverted_index.decompositions. | 175 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.06876659 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |