Yurii I. Lyubarskii and Kristian Seip
نویسندگان
چکیده
Assume that point evaluation is a bounded functional on H for each point z ∈ C, and also that H has the following symmetry property: H is closed under the operations f(z) 7→ f(z)(z− ζ)/(z− ζ) (provided f(ζ) = 0) and f(z) 7→ f(z). These assumptions ensure that H is a Hilbert space of entire functions in the sense of de Branges [4]. According to de Branges’ theory, there exists an entire function E belonging to the so-called Hermite-Biehler class (see below for definition) such that H = H(E) isometrically; here H(E) consists of all entire functions f such that both f(z)/E(z) and f(z)/E(z) belong to H of the upper half-plane, and the norm of f is given by
منابع مشابه
On Interpolation and Sampling in Hilbert Spaces of Analytic Functions
In this paper we give new proofs of some theorems due to Seip Seip Wallst en and Lyubarskii Seip on sequences of interpolation and sampling for spaces of analytic functions that are square integrable with respect to certain weights The results are also given in a somewhat more general setting Introduction In a series of recent papers Seip S Seip Wallst en S W and Lyuabarskii Seip L S have studi...
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