On a Class of Convolution Operators on a Finite Interval

G. M. Gubreev^a, G. D. Urum<sup>b

a</sup> Poltava National Technical University named after Yuri Kondratyuk
^b South Ukrainian State K. D. Ushynsky Pedagogical University

Abstract: In this paper, we state criteria for the completeness of root subspaces of convolution operators on a finite interval with kernels equal to the Fourier transform of the ratio of two entire functions of exponential type from special classes. We describe a class of entire functions with a regular (in a certain sense) distribution of roots.

Keywords: convolution operator, completeness of root subspaces, Fourier transform, entire function, function of exponential type, basis property of root vectors, Hilbert–Schmidt operator.

UDC: 517.5

Received: 16.09.2013

DOI: 10.4213/mzm10361

 English version: Mathematical Notes, 2014, 96:5, 647–650

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