Representations by Beurling Systems

We prove that a Beurling system with (Formula presented.) is an (Formula presented.) —basis in (Formula presented.) with an explicit dual system. Any function (Formula presented.) can be expanded as a series by the system (Formula presented.) For different summation methods, we characterize the oute...

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Detalles Bibliográficos
Autor: Ghazaryan, Ghazaros
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/714383
Acceso en línea:http://hdl.handle.net/10486/714383
https://dx.doi.org/10.3390/math11173663
Access Level:acceso abierto
Palabra clave:Beurling system
hardy spaces
kernels
outer function
representation of functions
summation basis
Matemáticas
Descripción
Sumario:We prove that a Beurling system with (Formula presented.) is an (Formula presented.) —basis in (Formula presented.) with an explicit dual system. Any function (Formula presented.) can be expanded as a series by the system (Formula presented.) For different summation methods, we characterize the outer functions F for which the expansion with respect to the corresponding Beurling system converges to f. Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesis