
Let \(E^ p\) denote the class of all entire functions of exponential type the restriction of which to the real axis lies in \(L^ p({\mathbb{R}})\). We give a simple example showing that if \((\lambda_ j)\) is a sequence of reals such that \(\Sigma | f(\lambda_ j)|^ p<\infty\) for every \(f\in E^ p\) then \((\lambda_ j)\) must be a finite union of separated sequences, thus resolving a ``problem'' in \textit{R. M. Young} ``An introduction to non-harmonic Fourier series'' (1980; Zbl 0493.42001).
Trigonometric moment problems in one variable harmonic analysis, example, \(H^p\)-classes, entire functions of exponential type
Trigonometric moment problems in one variable harmonic analysis, example, \(H^p\)-classes, entire functions of exponential type
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