A Generalization of the Kravchenko–Kotelnikov Theorem by Spectra of Compactly Supported Infinitely Differentiable Functions

A new generalization of the Kravchenko–Kotelnikov theorem by spectra of compactly supported infinitely differentiable functions is considered. These functions are solutions of linear integral equations of a special form. The spectrum of is a multiple infinite product of the spectra of the atomic fun...

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Bibliographic Details
Published in:Doklady. Mathematics 2019, Vol.99 (1), p.104-107
Main Authors: Budunova, K. A., Kravchenko, V. F., Pustovoit, V. I.
Format: Article
Language:English
Subjects:
Computer Science
Error analysis
Integral equations
Mathematics
Mathematics and Statistics
Spectra
Theorems
Truncation errors
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Summary:A new generalization of the Kravchenko–Kotelnikov theorem by spectra of compactly supported infinitely differentiable functions is considered. These functions are solutions of linear integral equations of a special form. The spectrum of is a multiple infinite product of the spectra of the atomic functions 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.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562419010150