Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis
| Autor: | Maria João Oliveira, Ludwig Streit, Yuri Kondratiev, Dmitri Finkelshtein, Eugene Lytvynov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Entire function
Nuclear space Sheffer sequence Context (language use) 010103 numerical & computational mathematics Topological space 01 natural sciences Combinatorics Sequence FOS: Mathematics Sheffer operator Appell sequence 0101 mathematics Complex Variables (math.CV) Infinite dimensional holomorphy Polynomials sequence of binomial type of polynomials of binomial type Mathematics Mathematics::Combinatorics Mathematics - Complex Variables Dual space Applied Mathematics 010102 general mathematics Infinite-dimensional holomorphy Nuclear and co-nuclear spaces Functional Analysis (math.FA) Spaces of entire functions Mathematics - Functional Analysis Analysis |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | For certain Sheffer sequences ( s n ) n = 0 ∞ on C , Grabiner (1988) proved that, for each α ∈ [ 0 , 1 ] , the corresponding Sheffer operator z n ↦ s n ( z ) extends to a linear self-homeomorphism of E min α ( C ) , the Frechet topological space of entire functions of order at most α and minimal type (when the order is equal to α > 0 ). In particular, every function f ∈ E min α ( C ) admits a unique decomposition f ( z ) = ∑ n = 0 ∞ c n s n ( z ) , and the series converges in the topology of E min α ( C ) . Within the context of a complex nuclear space Φ and its dual space Φ ′ , in this work we generalize Grabiner's result to the case of Sheffer operators corresponding to Sheffer sequences on Φ ′ . In particular, for Φ = Φ ′ = C n with n ≥ 2 , we obtain the multivariate extension of Grabiner's theorem. Furthermore, for an Appell sequence on a general co-nuclear space Φ ′ , we find a sufficient condition for the corresponding Sheffer operator to extend to a linear self-homeomorphism of E min α ( Φ ′ ) when α > 1 . The latter result is new even in the one-dimensional case. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|