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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| 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 |
| 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 |
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