On the second Hankel determinant of concave functions Article Swipe

PDF

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1512.03146

In the present paper, we will discuss the Hankel determinants $H(f) =a_2a_4-a_3^2$ of order 2 for normalized concave functions $f(z)=z+a_2z^2+a_3z^3+\dots$ with a pole at $p\in(0,1).$ Here, a meromorphic function is called concave if it maps the unit disk conformally onto a domain whose complement is convex. To this end, we will characterize the coefficient body of order 2 for the class of analytic functions $φ(z)$ on $|z|<1$ with $|φ|<1$ and $φ(p)=p.$ We believe that this is helpful for other extremal problems concerning $a_2, a_3, a_4$ for normalized concave functions with a pole at $p.$

Related Topics

Mathematics

Arithmetic

Mathematical Analysis

Geometry

Bessel Function

Concepts

Concave function Mathematics Hankel transform Hankel matrix Pure mathematics Arithmetic Mathematical analysis Geometry Bessel function Regular polygon

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1512.03146
PDF: https://arxiv.org/pdf/1512.03146
OA Status: green
References: 9
Related Works: 10
OpenAlex ID: https://openalex.org/W2270854735

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W2270854735

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.1512.03146

Digital Object Identifier
Title: On the second Hankel determinant of concave functions

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2015

Year of publication
Publication date: 2015-12-10

Full publication date if available
Authors: Rintaro Ohno, Toshiyuki Sugawa

List of authors in order
Landing page: https://arxiv.org/abs/1512.03146

Publisher landing page
PDF URL: https://arxiv.org/pdf/1512.03146

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/1512.03146

Direct OA link when available
Concepts: Concave function, Mathematics, Hankel transform, Hankel matrix, Pure mathematics, Arithmetic, Mathematical analysis, Geometry, Bessel function, Regular polygon

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

Total citation count in OpenAlex
References (count): 9

Number of works referenced by this work
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W2270854735
doi	https://doi.org/10.48550/arxiv.1512.03146
ids.doi	https://doi.org/10.48550/arxiv.1512.03146
ids.mag	2270854735
ids.openalex	https://openalex.org/W2270854735
fwci
type	preprint
title	On the second Hankel determinant of concave functions
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11822
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	0.9995999932289124
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2608
topics[0].subfield.display_name	Geometry and Topology
topics[0].display_name	Analytic and geometric function theory
topics[1].id	https://openalex.org/T11191
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9976999759674072
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2604
topics[1].subfield.display_name	Applied Mathematics
topics[1].display_name	Mathematical functions and polynomials
topics[2].id	https://openalex.org/T11564
topics[2].field.id	https://openalex.org/fields/26
topics[2].field.display_name	Mathematics
topics[2].score	0.9930999875068665
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2604
topics[2].subfield.display_name	Applied Mathematics
topics[2].display_name	Mathematical Inequalities and Applications
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C66690126
concepts[0].level	3
concepts[0].score	0.6020447015762329
concepts[0].wikidata	https://www.wikidata.org/wiki/Q2914302
concepts[0].display_name	Concave function
concepts[1].id	https://openalex.org/C33923547
concepts[1].level	0
concepts[1].score	0.574715793132782
concepts[1].wikidata	https://www.wikidata.org/wiki/Q395
concepts[1].display_name	Mathematics
concepts[2].id	https://openalex.org/C57640460
concepts[2].level	3
concepts[2].score	0.49735382199287415
concepts[2].wikidata	https://www.wikidata.org/wiki/Q155208
concepts[2].display_name	Hankel transform
concepts[3].id	https://openalex.org/C25023664
concepts[3].level	2
concepts[3].score	0.49187517166137695
concepts[3].wikidata	https://www.wikidata.org/wiki/Q1575637
concepts[3].display_name	Hankel matrix
concepts[4].id	https://openalex.org/C202444582
concepts[4].level	1
concepts[4].score	0.3787171244621277
concepts[4].wikidata	https://www.wikidata.org/wiki/Q837863
concepts[4].display_name	Pure mathematics
concepts[5].id	https://openalex.org/C94375191
concepts[5].level	1
concepts[5].score	0.3268882632255554
concepts[5].wikidata	https://www.wikidata.org/wiki/Q11205
concepts[5].display_name	Arithmetic
concepts[6].id	https://openalex.org/C134306372
concepts[6].level	1
concepts[6].score	0.2984730005264282
concepts[6].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[6].display_name	Mathematical analysis
concepts[7].id	https://openalex.org/C2524010
concepts[7].level	1
concepts[7].score	0.2752377688884735
concepts[7].wikidata	https://www.wikidata.org/wiki/Q8087
concepts[7].display_name	Geometry
concepts[8].id	https://openalex.org/C107706756
concepts[8].level	2
concepts[8].score	0.08713707327842712
concepts[8].wikidata	https://www.wikidata.org/wiki/Q219637
concepts[8].display_name	Bessel function
concepts[9].id	https://openalex.org/C112680207
concepts[9].level	2
concepts[9].score	0.07549887895584106
concepts[9].wikidata	https://www.wikidata.org/wiki/Q714886
concepts[9].display_name	Regular polygon
keywords[0].id	https://openalex.org/keywords/concave-function
keywords[0].score	0.6020447015762329
keywords[0].display_name	Concave function
keywords[1].id	https://openalex.org/keywords/mathematics
keywords[1].score	0.574715793132782
keywords[1].display_name	Mathematics
keywords[2].id	https://openalex.org/keywords/hankel-transform
keywords[2].score	0.49735382199287415
keywords[2].display_name	Hankel transform
keywords[3].id	https://openalex.org/keywords/hankel-matrix
keywords[3].score	0.49187517166137695
keywords[3].display_name	Hankel matrix
keywords[4].id	https://openalex.org/keywords/pure-mathematics
keywords[4].score	0.3787171244621277
keywords[4].display_name	Pure mathematics
keywords[5].id	https://openalex.org/keywords/arithmetic
keywords[5].score	0.3268882632255554
keywords[5].display_name	Arithmetic
keywords[6].id	https://openalex.org/keywords/mathematical-analysis
keywords[6].score	0.2984730005264282
keywords[6].display_name	Mathematical analysis
keywords[7].id	https://openalex.org/keywords/geometry
keywords[7].score	0.2752377688884735
keywords[7].display_name	Geometry
keywords[8].id	https://openalex.org/keywords/bessel-function
keywords[8].score	0.08713707327842712
keywords[8].display_name	Bessel function
keywords[9].id	https://openalex.org/keywords/regular-polygon
keywords[9].score	0.07549887895584106
keywords[9].display_name	Regular polygon
language	en
locations[0].id	pmh:oai:arXiv.org:1512.03146
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/1512.03146
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/1512.03146
locations[1].id	doi:10.48550/arxiv.1512.03146
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
locations[1].version
locations[1].raw_type	article
locations[1].license_id
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.1512.03146
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5025699581
authorships[0].author.orcid
authorships[0].author.display_name	Rintaro Ohno
authorships[0].author_position	first
authorships[0].raw_author_name	Rintaro Ohno
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5062945453
authorships[1].author.orcid	https://orcid.org/0000-0002-3429-5498
authorships[1].author.display_name	Toshiyuki Sugawa
authorships[1].author_position	last
authorships[1].raw_author_name	Toshiyuki Sugawa
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/1512.03146
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	On the second Hankel determinant of concave functions
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T11822
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	0.9995999932289124
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2608
primary_topic.subfield.display_name	Geometry and Topology
primary_topic.display_name	Analytic and geometric function theory
related_works	https://openalex.org/W1574625781, https://openalex.org/W2330799166, https://openalex.org/W2139768024, https://openalex.org/W881783402, https://openalex.org/W2042737795, https://openalex.org/W74469192, https://openalex.org/W2028837737, https://openalex.org/W2757898556, https://openalex.org/W3148685392, https://openalex.org/W2049807897
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:1512.03146
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/1512.03146
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/1512.03146
primary_location.id	pmh:oai:arXiv.org:1512.03146
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/1512.03146
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/1512.03146
publication_date	2015-12-10
publication_year	2015
referenced_works	https://openalex.org/W2099737046, https://openalex.org/W2047971998, https://openalex.org/W2075641980, https://openalex.org/W2030125978, https://openalex.org/W3098342838, https://openalex.org/W2081564218, https://openalex.org/W1979758165, https://openalex.org/W2000164127, https://openalex.org/W2160422022
referenced_works_count	9
abstract_inverted_index.2	14, 57
abstract_inverted_index.a	21, 26, 40, 90
abstract_inverted_index.In	0
abstract_inverted_index.To	46
abstract_inverted_index.We	71
abstract_inverted_index.at	23, 92
abstract_inverted_index.if	32
abstract_inverted_index.is	29, 44, 75
abstract_inverted_index.it	33
abstract_inverted_index.of	12, 55, 61
abstract_inverted_index.on	65
abstract_inverted_index.we	4, 49
abstract_inverted_index.and	69
abstract_inverted_index.for	15, 58, 77, 85
abstract_inverted_index.the	1, 7, 35, 52, 59
abstract_inverted_index.$p.$	93
abstract_inverted_index.a_3,	83
abstract_inverted_index.a_4$	84
abstract_inverted_index.body	54
abstract_inverted_index.disk	37
abstract_inverted_index.end,	48
abstract_inverted_index.maps	34
abstract_inverted_index.onto	39
abstract_inverted_index.pole	22, 91
abstract_inverted_index.that	73
abstract_inverted_index.this	47, 74
abstract_inverted_index.unit	36
abstract_inverted_index.will	5, 50
abstract_inverted_index.with	20, 67, 89
abstract_inverted_index.$H(f)	10
abstract_inverted_index.$a_2,	82
abstract_inverted_index.Here,	25
abstract_inverted_index.class	60
abstract_inverted_index.order	13, 56
abstract_inverted_index.other	78
abstract_inverted_index.whose	42
abstract_inverted_index.Hankel	8
abstract_inverted_index.called	30
abstract_inverted_index.domain	41
abstract_inverted_index.paper,	3
abstract_inverted_index.$φ(z)$	64
abstract_inverted_index.believe	72
abstract_inverted_index.concave	17, 31, 87
abstract_inverted_index.convex.	45
abstract_inverted_index.discuss	6
abstract_inverted_index.helpful	76
abstract_inverted_index.present	2
abstract_inverted_index.analytic	62
abstract_inverted_index.extremal	79
abstract_inverted_index.function	28
abstract_inverted_index.problems	80
abstract_inverted_index.functions	18, 63, 88
abstract_inverted_index.$\|z\|<1$	66
abstract_inverted_index.$φ(p)=p.$	70
abstract_inverted_index.complement	43
abstract_inverted_index.concerning	81
abstract_inverted_index.normalized	16, 86
abstract_inverted_index.$\|φ\|<1$	68
abstract_inverted_index.coefficient	53
abstract_inverted_index.conformally	38
abstract_inverted_index.meromorphic	27
abstract_inverted_index.$p\in(0,1).$	24
abstract_inverted_index.characterize	51
abstract_inverted_index.determinants	9
abstract_inverted_index.=a_2a_4-a_3^2$	11
abstract_inverted_index.$f(z)=z+a_2z^2+a_3z^3+\dots$	19
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	2
citation_normalized_percentile