Non-oscillating Paley-Wiener functions |
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Authors: | I. V. Ostrovskii A. Ulanovskii |
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Affiliation: | (1) Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey;(2) Verkin Institute for Low Temperature Physics and Engineering, 61103 Kharkov, Ukraine;(3) Stavanger University College, P.O. Box 2557 Ullandhaug, 4091 Stavanger, Norway |
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Abstract: | A non-oscillating Paley-Wiener function is a real entire functionf of exponential type belonging toL 2(R) and such that each derivativef (n),n=0, 1, 2,…, has only a finite number of real zeros. It is established that the class of such functions is non-empty and contains functions of arbitrarily fast decay onR allowed by the convergence of the logarithmic integral. It is shown that the Fourier transform of a non-oscillating Paley-Wiener function must be infinitely differentiable outside the origin. We also give close to best possible asymptotic (asn→∞) estimates of the number of real zeros of then-th derivative of a functionf of the class and the size of the smallest interval containing these zeros. |
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