Doklady Mathematics. Vol. 99, No. 1, Pages 104-107, 2019

K. A. Budunova^a^,*, V. F. Kravchenko^a, and Academician of the RAS V. I. Pustovoit^b
Translated by N. Berestova

^aKotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, 125009 Russia

^bScientific and Technological Center of Unique Instrumentation, Russian Academy of Sciences, Moscow, 117342 Russia

Abstract—A new generalization of the Kravchenko–Kotelnikov theorem by spectra of compactly supported infinitely differentiable functions $h_{{\mathbf{a}}}^{{(m)}}(x)$ is considered. These functions are solutions of linear integral equations of a special form. The spectrum of $h_{{\mathbf{a}}}^{{(m)}}(x)$ is a multiple infinite product of the spectra of the atomic functions ${{h}_{a}}(x)$ dilated with respect to the argument. The resulting generalized series is characterized by fast convergence, which is confirmed by the truncation error bound presented in the study and by the results of a numerical experiment.

A Generalization of the Kravchenko–Kotelnikov Theorem by Spectra of Compactly Supported Infinitely Differentiable Functions ${\mathbf{h}}_{a}^{{(m)}}(x)$