Artículo
Hardy space of translated Dirichlet series
Fecha de publicación:
03/2021
Editorial:
Springer
Revista:
Mathematische Zeitschrift
ISSN:
0025-5874
e-ISSN:
1432-1823
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We study the Hardy space of translated Dirichlet series H+. It consists on those Dirichlet series ∑ ann-s such that for some (equivalently, every) 1 ≤ p< ∞, the translation ∑ann-(s+1σ) belongs to the Hardy space Hp for every σ> 0. We prove that this set, endowed with the topology induced by the seminorms {‖·‖2,k}k∈N (where ‖ ∑ ann-s‖ 2,k is defined as ‖∑ann-(s+1k)‖H2), is a Fréchet space which is Schwartz and non nuclear. Moreover, the Dirichlet monomials {n-s}n∈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.
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Fernández Vidal, Tomás Ariel; Galicer, Daniel Eric; Mereb, Martin; Sevilla Peris, Pablo; Hardy space of translated Dirichlet series; Springer; Mathematische Zeitschrift; 299; 1-2; 3-2021; 1103-1129
Compartir
Altmétricas