Distance formulas on weighted Banach spaces of analytic functions
[EN] Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function f0 in the Banach space Hv all analytic functions f such that v|f| is bounded, the distance of f0 to the subspace Hv0 of Hv of all the functions g such that v|g| vanishes at in...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/155435 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/155435 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach spaces of analytic functions Weight Distance Bloch functions MATEMATICA APLICADA |
| Sumario: | [EN] Let v be a radial weight function on the unit disc or on the complex plane. It is shown that for each analytic function f0 in the Banach space Hv all analytic functions f such that v|f| is bounded, the distance of f0 to the subspace Hv0 of Hv of all the functions g such that v|g| vanishes at infinity is attained at a function g0Hv0. Moreover a simple, direct proof of the formula of the distance of f to Hv0 due to Perfekt is presented. As a consequence the corresponding results for weighted Bloch spaces are obtained. |
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