Kernel Smoothing Operators on Thick Open Domains Article Swipe

PDF

Dimitrios Giannakis , Mohammad Javad Latifi Jebelli ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2403.00173

We define the notion of a thick open set $Ω$ in a Euclidean space and show that a local Hardy-Littlewood inequality holds in $L^p(Ω)$, $p \in (1, \infty]$. We then establish pointwise and $L^p(Ω)$ convergence for families of convolution operators with a Markov normalization on $Ω$. We demonstrate application of such smoothing operators to piecewise-continuous density, velocity, and stress fields from discrete element models of sea ice dynamics.

Related Topics

Computer Science

Mathematics

Artificial Intelligence

Kernel Method

Computer Vision

Support Vector Machine

Concepts

Kernel (algebra) Smoothing Computer science Kernel smoother Mathematics Artificial intelligence Kernel method Pure mathematics Computer vision Radial basis function kernel Support vector machine

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2403.00173
PDF: https://arxiv.org/pdf/2403.00173
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4392425851

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4392425851

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2403.00173

Digital Object Identifier
Title: Kernel Smoothing Operators on Thick Open Domains

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2024

Year of publication
Publication date: 2024-02-29

Full publication date if available
Authors: Dimitrios Giannakis, Mohammad Javad Latifi Jebelli

List of authors in order
Landing page: https://arxiv.org/abs/2403.00173

Publisher landing page
PDF URL: https://arxiv.org/pdf/2403.00173

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2403.00173

Direct OA link when available
Concepts: Kernel (algebra), Smoothing, Computer science, Kernel smoother, Mathematics, Artificial intelligence, Kernel method, Pure mathematics, Computer vision, Radial basis function kernel, Support vector machine

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4392425851
doi	https://doi.org/10.48550/arxiv.2403.00173
ids.doi	https://doi.org/10.48550/arxiv.2403.00173
ids.openalex	https://openalex.org/W4392425851
fwci
type	preprint
title	Kernel Smoothing Operators on Thick Open Domains
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11205
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	0.9944000244140625
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2610
topics[0].subfield.display_name	Mathematical Physics
topics[0].display_name	Numerical methods in inverse problems
topics[1].id	https://openalex.org/T12100
topics[1].field.id	https://openalex.org/fields/17
topics[1].field.display_name	Computer Science
topics[1].score	0.9937999844551086
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/1703
topics[1].subfield.display_name	Computational Theory and Mathematics
topics[1].display_name	Advanced Mathematical Modeling in Engineering
topics[2].id	https://openalex.org/T10339
topics[2].field.id	https://openalex.org/fields/22
topics[2].field.display_name	Engineering
topics[2].score	0.9690999984741211
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2206
topics[2].subfield.display_name	Computational Mechanics
topics[2].display_name	Advanced Numerical Methods in Computational Mathematics
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C74193536
concepts[0].level	2
concepts[0].score	0.6982607245445251
concepts[0].wikidata	https://www.wikidata.org/wiki/Q574844
concepts[0].display_name	Kernel (algebra)
concepts[1].id	https://openalex.org/C3770464
concepts[1].level	2
concepts[1].score	0.6928739547729492
concepts[1].wikidata	https://www.wikidata.org/wiki/Q775963
concepts[1].display_name	Smoothing
concepts[2].id	https://openalex.org/C41008148
concepts[2].level	0
concepts[2].score	0.5059756636619568
concepts[2].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[2].display_name	Computer science
concepts[3].id	https://openalex.org/C27406209
concepts[3].level	5
concepts[3].score	0.4799114167690277
concepts[3].wikidata	https://www.wikidata.org/wiki/Q6394203
concepts[3].display_name	Kernel smoother
concepts[4].id	https://openalex.org/C33923547
concepts[4].level	0
concepts[4].score	0.38068386912345886
concepts[4].wikidata	https://www.wikidata.org/wiki/Q395
concepts[4].display_name	Mathematics
concepts[5].id	https://openalex.org/C154945302
concepts[5].level	1
concepts[5].score	0.3528990149497986
concepts[5].wikidata	https://www.wikidata.org/wiki/Q11660
concepts[5].display_name	Artificial intelligence
concepts[6].id	https://openalex.org/C122280245
concepts[6].level	3
concepts[6].score	0.2715423107147217
concepts[6].wikidata	https://www.wikidata.org/wiki/Q620622
concepts[6].display_name	Kernel method
concepts[7].id	https://openalex.org/C202444582
concepts[7].level	1
concepts[7].score	0.17856624722480774
concepts[7].wikidata	https://www.wikidata.org/wiki/Q837863
concepts[7].display_name	Pure mathematics
concepts[8].id	https://openalex.org/C31972630
concepts[8].level	1
concepts[8].score	0.1471659541130066
concepts[8].wikidata	https://www.wikidata.org/wiki/Q844240
concepts[8].display_name	Computer vision
concepts[9].id	https://openalex.org/C75866337
concepts[9].level	4
concepts[9].score	0.12599080801010132
concepts[9].wikidata	https://www.wikidata.org/wiki/Q7280263
concepts[9].display_name	Radial basis function kernel
concepts[10].id	https://openalex.org/C12267149
concepts[10].level	2
concepts[10].score	0.048664361238479614
concepts[10].wikidata	https://www.wikidata.org/wiki/Q282453
concepts[10].display_name	Support vector machine
keywords[0].id	https://openalex.org/keywords/kernel
keywords[0].score	0.6982607245445251
keywords[0].display_name	Kernel (algebra)
keywords[1].id	https://openalex.org/keywords/smoothing
keywords[1].score	0.6928739547729492
keywords[1].display_name	Smoothing
keywords[2].id	https://openalex.org/keywords/computer-science
keywords[2].score	0.5059756636619568
keywords[2].display_name	Computer science
keywords[3].id	https://openalex.org/keywords/kernel-smoother
keywords[3].score	0.4799114167690277
keywords[3].display_name	Kernel smoother
keywords[4].id	https://openalex.org/keywords/mathematics
keywords[4].score	0.38068386912345886
keywords[4].display_name	Mathematics
keywords[5].id	https://openalex.org/keywords/artificial-intelligence
keywords[5].score	0.3528990149497986
keywords[5].display_name	Artificial intelligence
keywords[6].id	https://openalex.org/keywords/kernel-method
keywords[6].score	0.2715423107147217
keywords[6].display_name	Kernel method
keywords[7].id	https://openalex.org/keywords/pure-mathematics
keywords[7].score	0.17856624722480774
keywords[7].display_name	Pure mathematics
keywords[8].id	https://openalex.org/keywords/computer-vision
keywords[8].score	0.1471659541130066
keywords[8].display_name	Computer vision
keywords[9].id	https://openalex.org/keywords/radial-basis-function-kernel
keywords[9].score	0.12599080801010132
keywords[9].display_name	Radial basis function kernel
keywords[10].id	https://openalex.org/keywords/support-vector-machine
keywords[10].score	0.048664361238479614
keywords[10].display_name	Support vector machine
language	en
locations[0].id	pmh:oai:arXiv.org:2403.00173
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2403.00173
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2403.00173
locations[1].id	doi:10.48550/arxiv.2403.00173
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	cc-by
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id	https://openalex.org/licenses/cc-by
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2403.00173
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5076538541
authorships[0].author.orcid	https://orcid.org/0000-0002-4220-0313
authorships[0].author.display_name	Dimitrios Giannakis
authorships[0].author_position	first
authorships[0].raw_author_name	Giannakis, Dimitrios
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5033797478
authorships[1].author.orcid	https://orcid.org/0000-0002-0088-266X
authorships[1].author.display_name	Mohammad Javad Latifi Jebelli
authorships[1].author_position	last
authorships[1].raw_author_name	Jebelli, Mohammad Javad Latifi
authorships[1].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/2403.00173
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Kernel Smoothing Operators on Thick Open Domains
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T11205
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	0.9944000244140625
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2610
primary_topic.subfield.display_name	Mathematical Physics
primary_topic.display_name	Numerical methods in inverse problems
related_works	https://openalex.org/W2552416899, https://openalex.org/W2999721917, https://openalex.org/W4287906215, https://openalex.org/W4206381862, https://openalex.org/W1833023352, https://openalex.org/W2079476921, https://openalex.org/W2420851703, https://openalex.org/W2740619373, https://openalex.org/W2114275252, https://openalex.org/W3088749410
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2403.00173
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/2403.00173
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/2403.00173
primary_location.id	pmh:oai:arXiv.org:2403.00173
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2403.00173
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2403.00173
publication_date	2024-02-29
publication_year	2024
referenced_works_count	0
abstract_inverted_index.a	5, 11, 17, 41
abstract_inverted_index.$p	24
abstract_inverted_index.We	0, 28, 46
abstract_inverted_index.in	10, 22
abstract_inverted_index.of	4, 37, 49, 64
abstract_inverted_index.on	44
abstract_inverted_index.to	53
abstract_inverted_index.(1,	26
abstract_inverted_index.\in	25
abstract_inverted_index.and	14, 32, 57
abstract_inverted_index.for	35
abstract_inverted_index.ice	66
abstract_inverted_index.sea	65
abstract_inverted_index.set	8
abstract_inverted_index.the	2
abstract_inverted_index.$Ω$	9
abstract_inverted_index.from	60
abstract_inverted_index.open	7
abstract_inverted_index.show	15
abstract_inverted_index.such	50
abstract_inverted_index.that	16
abstract_inverted_index.then	29
abstract_inverted_index.with	40
abstract_inverted_index.$Ω$.	45
abstract_inverted_index.holds	21
abstract_inverted_index.local	18
abstract_inverted_index.space	13
abstract_inverted_index.thick	6
abstract_inverted_index.Markov	42
abstract_inverted_index.define	1
abstract_inverted_index.fields	59
abstract_inverted_index.models	63
abstract_inverted_index.notion	3
abstract_inverted_index.stress	58
abstract_inverted_index.element	62
abstract_inverted_index.density,	55
abstract_inverted_index.discrete	61
abstract_inverted_index.families	36
abstract_inverted_index.$L^p(Ω)$	33
abstract_inverted_index.Euclidean	12
abstract_inverted_index.\infty]$.	27
abstract_inverted_index.dynamics.	67
abstract_inverted_index.establish	30
abstract_inverted_index.operators	39, 52
abstract_inverted_index.pointwise	31
abstract_inverted_index.smoothing	51
abstract_inverted_index.velocity,	56
abstract_inverted_index.$L^p(Ω)$,	23
abstract_inverted_index.inequality	20
abstract_inverted_index.application	48
abstract_inverted_index.convergence	34
abstract_inverted_index.convolution	38
abstract_inverted_index.demonstrate	47
abstract_inverted_index.normalization	43
abstract_inverted_index.Hardy-Littlewood	19
abstract_inverted_index.piecewise-continuous	54
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	2
citation_normalized_percentile