Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications

Autores
Aljawi, Salma; Conde, Cristian Marcelo; Dragomir, Silvestru Sever; Feki, Kais
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present work, we give a new proof of the well-known Selberg’s inequality in complex Hilbert spaces from an operator-theoretic perspective, establishing its fundamental equivalence with the Cauchy–Bunyakovsky–Schwarz inequality. We also derive several lower and upper bounds for the Selberg operator, including its norm estimates, refining classical results such as de Bruijn’s and Bohr’s inequalities. Additionally, we revisit a recent claim in the literature, providing a clarification of the conditions under which Selberg’s inequality extends to abstract bilinear forms.
Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento;
Fil: Dragomir, Silvestru Sever. La Trobe University; Australia
Fil: Feki, Kais. Najran University; Arabia Saudita
Materia
Selberg’s inequality
Selberg operator
Cauchy–Bunyakovsky–Schwarz inequality
bilinear forms
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/277970
Acceder
id CONICETDig_db2c94fe54a696630d5a02e3aef90a75
oai_identifier_str oai:ri.conicet.gov.ar:11336/277970
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with ApplicationsAljawi, SalmaConde, Cristian MarceloDragomir, Silvestru SeverFeki, KaisSelberg’s inequalitySelberg operatorCauchy–Bunyakovsky–Schwarz inequalitybilinear formshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the present work, we give a new proof of the well-known Selberg’s inequality in complex Hilbert spaces from an operator-theoretic perspective, establishing its fundamental equivalence with the Cauchy–Bunyakovsky–Schwarz inequality. We also derive several lower and upper bounds for the Selberg operator, including its norm estimates, refining classical results such as de Bruijn’s and Bohr’s inequalities. Additionally, we revisit a recent claim in the literature, providing a clarification of the conditions under which Selberg’s inequality extends to abstract bilinear forms.Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia SauditaFil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento;Fil: Dragomir, Silvestru Sever. La Trobe University; AustraliaFil: Feki, Kais. Najran University; Arabia SauditaMultidisciplinary Digital Publishing Institute2025-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/277970Aljawi, Salma; Conde, Cristian Marcelo; Dragomir, Silvestru Sever; Feki, Kais; Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications; Multidisciplinary Digital Publishing Institute; Axioms; 14; 8; 7-2025; 1-222075-1680CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2075-1680/14/8/575info:eu-repo/semantics/altIdentifier/doi/10.3390/axioms14080575info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T13:37:51Zoai:ri.conicet.gov.ar:11336/277970instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-12-23 13:37:51.303CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
title Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
spellingShingle Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
Aljawi, Salma
Selberg’s inequality
Selberg operator
Cauchy–Bunyakovsky–Schwarz inequality
bilinear forms
title_short Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
title_full Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
title_fullStr Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
title_full_unstemmed Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
title_sort Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications
dc.creator.none.fl_str_mv Aljawi, Salma
Conde, Cristian Marcelo
Dragomir, Silvestru Sever
Feki, Kais
author Aljawi, Salma
author_facet Aljawi, Salma
Conde, Cristian Marcelo
Dragomir, Silvestru Sever
Feki, Kais
author_role author
author2 Conde, Cristian Marcelo
Dragomir, Silvestru Sever
Feki, Kais
author2_role author
author
author
dc.subject.none.fl_str_mv Selberg’s inequality
Selberg operator
Cauchy–Bunyakovsky–Schwarz inequality
bilinear forms
topic Selberg’s inequality
Selberg operator
Cauchy–Bunyakovsky–Schwarz inequality
bilinear forms
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the present work, we give a new proof of the well-known Selberg’s inequality in complex Hilbert spaces from an operator-theoretic perspective, establishing its fundamental equivalence with the Cauchy–Bunyakovsky–Schwarz inequality. We also derive several lower and upper bounds for the Selberg operator, including its norm estimates, refining classical results such as de Bruijn’s and Bohr’s inequalities. Additionally, we revisit a recent claim in the literature, providing a clarification of the conditions under which Selberg’s inequality extends to abstract bilinear forms.
Fil: Aljawi, Salma. Princess Nourah Bint Abdulrahman University; Arabia Saudita
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Area de Matematica (area de Matematica) ; Instituto de Ciencias ; Universidad Nacional de General Sarmiento;
Fil: Dragomir, Silvestru Sever. La Trobe University; Australia
Fil: Feki, Kais. Najran University; Arabia Saudita
description In the present work, we give a new proof of the well-known Selberg’s inequality in complex Hilbert spaces from an operator-theoretic perspective, establishing its fundamental equivalence with the Cauchy–Bunyakovsky–Schwarz inequality. We also derive several lower and upper bounds for the Selberg operator, including its norm estimates, refining classical results such as de Bruijn’s and Bohr’s inequalities. Additionally, we revisit a recent claim in the literature, providing a clarification of the conditions under which Selberg’s inequality extends to abstract bilinear forms.
publishDate 2025
dc.date.none.fl_str_mv 2025-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/277970
Aljawi, Salma; Conde, Cristian Marcelo; Dragomir, Silvestru Sever; Feki, Kais; Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications; Multidisciplinary Digital Publishing Institute; Axioms; 14; 8; 7-2025; 1-22
2075-1680
CONICET Digital
CONICET
url http://hdl.handle.net/11336/277970
identifier_str_mv Aljawi, Salma; Conde, Cristian Marcelo; Dragomir, Silvestru Sever; Feki, Kais; Selberg’s Inequality and Selberg Operator Bounds in Hilbert Spaces with Applications; Multidisciplinary Digital Publishing Institute; Axioms; 14; 8; 7-2025; 1-22
2075-1680
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2075-1680/14/8/575
info:eu-repo/semantics/altIdentifier/doi/10.3390/axioms14080575
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1852335272615739392
score 12.952241

Publicaciones similares