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Nonlocal almost differential operators and interpolation by functions with sparse spectrum. (English. Russian original) Zbl 0622.42007
Math. USSR, Sb. 56, 131-140 (1987); translation from Mat. Sb., Nov. Ser. 128(170), No. 1, 133-138 (1985).
This paper contains two main results. The first disproves a hypothesis of de Branges by constructing a nonlocal convolution operator \({\mathcal L}_ E={\mathcal F}^{-1}E {\mathcal F}\) whose symbol E is an entire function of zero order. The second gives a sufficient condition for a symmetric set A of integral numbers to satisfy the property that every function in the Weiner’s algebra coincides on some set with a function of the same class whose spectrum lies in A. This is used to disprove another hypothesis of de Branges.
Reviewer: A.H.Nasr
MSC:
42A45 Multipliers in one variable harmonic analysis
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