On differentiability and analyticity of positive definite functions

Bibliographic Details
Main Author: Buescu, Jorge
Publication Date: 2011
Other Authors: Paixão, António
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.21/674
Summary: We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.
id RCAP_acfc506175595b4d8bd008fdae2da7c8
oai_identifier_str oai:repositorio.ipl.pt:10400.21/674
network_acronym_str RCAP
network_name_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository_id_str https://opendoar.ac.uk/repository/7160
spelling On differentiability and analyticity of positive definite functionsPositive definite functionsInequalitiesAnalytic functionsWe derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.Academic Press Inc Elsevier ScienceRCIPLBuescu, JorgePaixão, António2011-11-28T13:23:09Z2011-03-012011-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/674eng0022-247Xinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-12T08:36:20Zoai:repositorio.ipl.pt:10400.21/674Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T19:56:47.848072Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv On differentiability and analyticity of positive definite functions
title On differentiability and analyticity of positive definite functions
spellingShingle On differentiability and analyticity of positive definite functions
Buescu, Jorge
Positive definite functions
Inequalities
Analytic functions
title_short On differentiability and analyticity of positive definite functions
title_full On differentiability and analyticity of positive definite functions
title_fullStr On differentiability and analyticity of positive definite functions
title_full_unstemmed On differentiability and analyticity of positive definite functions
title_sort On differentiability and analyticity of positive definite functions
author Buescu, Jorge
author_facet Buescu, Jorge
Paixão, António
author_role author
author2 Paixão, António
author2_role author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Buescu, Jorge
Paixão, António
dc.subject.por.fl_str_mv Positive definite functions
Inequalities
Analytic functions
topic Positive definite functions
Inequalities
Analytic functions
description We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.
publishDate 2011
dc.date.none.fl_str_mv 2011-11-28T13:23:09Z
2011-03-01
2011-03-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.21/674
url http://hdl.handle.net/10400.21/674
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-247X
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833598408836775936

Similar Items