A. Sh. Shaldanbaev, M. I. Akylbaev, M. T. Shomanbayeva, A. A. Shaldanbayeva, “Criterion for the Volterra property of the Cauchy problem for the pantograph equation”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 171,Pages <nobr>140

Criterion for the Volterra property of the Cauchy problem for the pantograph equation

A. Sh. Shaldanbaev^a, M. I. Akylbaev^b, M. T. Shomanbayeva^c, A. A. Shaldanbayeva^b

^a International University SILKWAY
^b Regional Social and Innovative University
^c M. O. Auezov South Kazakhstan State University

Abstract: In this paper, spectral properties of the Cauchy problem of the pantograph equation are examined and the boundary of the parameter range is established at which the problem remains a Volterra problem.

Keywords: pantograph equation, spectrum, complete continuity, nuclearity, Hilbert–Schmidt operator, operator trace formula, Gaal formula.

UDC: 517.929

MSC: 34K06, 34K08

DOI: 10.36535/0233-6723-2019-171-140-145