On analytic sampling theory

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:171

Article

García, AG ; Littlejohn, LL

关键词: analytic Hilbert space-valued functions;    reproducing kernel Hilbert spaces;    sampling series;   

DOI  :  10.1016/j.cam.2004.01.016

来源: Elsevier

【 摘 要 】

Let (H, ((.),(.))(H)) be a complex, separable Hilbert space with orthonormal basis {x(n)}(n=1)(infinity) and let Omega be a domain in C, the field of complex numbers. Suppose K is a H-valued function defined on Omega. For each x (E H, define f(x)(z) = (K(z), X)(H) and let H denote the collection of all such functions f(x). In this paper, we endow H with a structure of a reproducing kernel Hilbert space. Furthermore, we show that each element in H is analytic on Omega if and only if K is analytic on Omega or, equivalently, if and only if (K(z), x(n)) is analytic for each n is an element of N and is bounded on all compact subsets of Omega. In this setting, an abstract version of the analytic Kramer theorem is exhibited. Some examples considering different H spaces are given to illustrate these new results. (C) 2004 Published by Elsevier B.V.

【 授权许可】

Free