Hankel transforms of general monotone functions

We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel-Olivier test for real- valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not...

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Detalles Bibliográficos
Autor: Debernardi Pinos, Alberto|||0000-0002-2647-5851
Tipo de recurso: capítulo de libro
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:288468
Acceso en línea:https://ddd.uab.cat/record/288468
https://dx.doi.org/urn:doi:10.1007/978-3-030-12277-5_5
Access Level:acceso abierto
Palabra clave:Hankel transform
Boundedness
Uniform convergence
General monotonicity
Cosine series
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spelling Hankel transforms of general monotone functionsDebernardi Pinos, Alberto|||0000-0002-2647-5851Hankel transformBoundednessUniform convergenceGeneral monotonicityCosine seriesWe show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel-Olivier test for real- valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series.Birkhäuser 22019-01-0120192019-01-01Capítol de llibrehttp://purl.org/coar/resource_type/c_3248AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/bookPartapplication/pdfhttps://ddd.uab.cat/record/288468https://dx.doi.org/urn:doi:10.1007/978-3-030-12277-5_5reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengEuropean Commission https://doi.org/10.13039/501100000780 713927Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-87409-Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2884682026-06-06T12:50:31Z
dc.title.none.fl_str_mv Hankel transforms of general monotone functions
title Hankel transforms of general monotone functions
spellingShingle Hankel transforms of general monotone functions
Debernardi Pinos, Alberto|||0000-0002-2647-5851
Hankel transform
Boundedness
Uniform convergence
General monotonicity
Cosine series
title_short Hankel transforms of general monotone functions
title_full Hankel transforms of general monotone functions
title_fullStr Hankel transforms of general monotone functions
title_full_unstemmed Hankel transforms of general monotone functions
title_sort Hankel transforms of general monotone functions
dc.creator.none.fl_str_mv Debernardi Pinos, Alberto|||0000-0002-2647-5851
author Debernardi Pinos, Alberto|||0000-0002-2647-5851
author_facet Debernardi Pinos, Alberto|||0000-0002-2647-5851
author_role author
dc.subject.none.fl_str_mv Hankel transform
Boundedness
Uniform convergence
General monotonicity
Cosine series
topic Hankel transform
Boundedness
Uniform convergence
General monotonicity
Cosine series
description We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel-Olivier test for real- valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series.
publishDate 2019
dc.date.none.fl_str_mv 2
2019-01-01
2019
2019-01-01
dc.type.none.fl_str_mv Capítol de llibre
http://purl.org/coar/resource_type/c_3248
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/288468
https://dx.doi.org/urn:doi:10.1007/978-3-030-12277-5_5
url https://ddd.uab.cat/record/288468
https://dx.doi.org/urn:doi:10.1007/978-3-030-12277-5_5
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission https://doi.org/10.13039/501100000780 713927
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-87409-P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Birkhäuser
publisher.none.fl_str_mv Birkhäuser
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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