منابع مشابه
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We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de Branges’ theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a cla...
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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...
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ژورنال
عنوان ژورنال: Målbryting
سال: 2019
ISSN: 1500-8576
DOI: 10.7557/17.4766