Affiliation:
1. Department of Mathematics and Economics, Drohobych Ivan Franko State Pedagogical University, Drohobych, Ukraine
Abstract
In this paper, we study an integral representation of some class E2,+ of
even entire functions of exponential type ? ? 1. We also obtain an analog of
the Paley-Wiener theorem related to the class E2,+. In addition, we find
necessary and sufficient conditions for the completeness of a system n sk ?
xsk J?3/2(xsk) : k ? N o in the space L2((0; 1); x2dx), where J?3/2 be the
Bessel function of the first kind of index ?3/2, (sk)k?N be a sequence of
distinct nonzero complex numbers and L2((0; 1); x2dx) be the weighted
Lebesgue space of all measurable functions f : (0; 1) ? C satisfying R 1 0
x2| f (x)|2 dx < +?. Those results are formulated in terms of sequences of
zeros of functions from the class E2,+. We also obtain some other sufficient
conditions for the completeness of the considered system of Bessel
functions. Our results complement similar results on completeness of the
systems of Bessel functions of index ? < ?1, ? ? Z.
Publisher
National Library of Serbia
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