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dc.contributor.author | Fernández Vidal, Tomás | es_ES |
dc.contributor.author | Galicer, Daniel | es_ES |
dc.contributor.author | Mereb, Martín | es_ES |
dc.contributor.author | Sevilla Peris, Pablo | es_ES |
dc.date.accessioned | 2022-11-08T19:01:30Z | |
dc.date.available | 2022-11-08T19:01:30Z | |
dc.date.issued | 2021-10 | es_ES |
dc.identifier.issn | 0025-5874 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/189476 | |
dc.description.abstract | [EN] We study the Hardy space of translated Dirichlet series H+. It consists on those Dirichlet series Sigma a(n)n(-s) such that for some (equivalently, every) 1 <= p < infinity, the translation Sigma a(n)n(-(s+ 1/sigma)) belongs to the Hardy space H-p for every sigma > 0. We prove that this set, endowed with the topology induced by the seminorms {parallel to center dot parallel to(2,k)}(k is an element of N) (where parallel to Sigma a(n)n(-s) parallel to(2,k) is defined as parallel to Sigma a(n)n(-(s+ 1/k))parallel to(H2)), is a Frechet space which is Schwartz and non nuclear. Moreover, the Dirichlet monomials {n(-s)}(n is an element of N) are an unconditional Schauder basis of H+. We also explore the connection of this new space with spaces of holomorphic functions on infinite-dimensional spaces. In the spirit of Gordon and Hedenmalm's work, we completely characterize the composition operator on the Hardy space of translated Dirichlet series. Moreover, we study the superposition operators on H+ and show that every polynomial defines an operator of this kind. We present certain sufficient conditions on the coefficients of an entire function to define a superposition operator. Relying on number theory techniques we exhibit some examples which do not provide superposition operators. We finally look at the action of the differentiation and integration operators on these spaces. | es_ES |
dc.description.sponsorship | We would like to warmly thank Jose Bonet, Andreas Defant and Manuel Maestre for enlightening remarks and comments and fruitful discussions that improved the paper. We would also like to thank the referees for their careful reading and helpful comments. The research of T. Fernandez Vidal was supported by PICT 2015-2299. The research of D. Galicer was partially supported by CONICET-PIP 11220130100329CO and 2018-04250. The research of M. Mereb was partially supported by CONICET-PIP 11220130100073CO and PICT 2018-03511. The research of P. Sevilla-Peris was supported by MICINN and FEDER Project MTM2017-83262-C2-1-P and MECD Grant PRX17/00040. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Springer-Verlag | es_ES |
dc.relation.ispartof | Mathematische Zeitschrift | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Dirichlet series | es_ES |
dc.subject | Hardy space | es_ES |
dc.subject | Frechet space | es_ES |
dc.subject | Composition operator | es_ES |
dc.subject | Superposition operator | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Hardy space of translated Dirichlet series | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1007/s00209-021-02700-2 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83262-C2-1-P/ES/ANALISIS COMPLEJO Y GEOMETRIA EN ESPACIOS DE BANACH/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/ANPCyT//PICT 2018-03511/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/ANPCyT//PICT 2015-2299/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/CONICET//2018-04250/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/CONICET//PIP 11220130100329CO/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/CONICET//PIP 11220130100073CO/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MECD//PRX17%2F00040/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural - Escola Tècnica Superior d'Enginyeria Agronòmica i del Medi Natural | es_ES |
dc.description.bibliographicCitation | Fernández Vidal, T.; Galicer, D.; Mereb, M.; Sevilla Peris, P. (2021). Hardy space of translated Dirichlet series. Mathematische Zeitschrift. 299:1103-1129. https://doi.org/10.1007/s00209-021-02700-2 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1007/s00209-021-02700-2 | es_ES |
dc.description.upvformatpinicio | 1103 | es_ES |
dc.description.upvformatpfin | 1129 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 299 | es_ES |
dc.relation.pasarela | S\460807 | es_ES |
dc.contributor.funder | European Regional Development Fund | es_ES |
dc.contributor.funder | Ministerio de Educación, Cultura y Deporte | es_ES |
dc.contributor.funder | Ministerio de Economía, Industria y Competitividad | es_ES |
dc.contributor.funder | Agencia Nacional de Promoción Científica y Tecnológica, Argentina | es_ES |
dc.contributor.funder | Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina | es_ES |
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