Generalization of Kravchenko—Kotelnikov theorem by spectra of compactly supported infinitely differentiable functions

Cover Page

Cite item

Abstract

New generalization of KravchenkoKotelnikov theorem by spectra of compactly supported infinitely differentiable functions is discussed. These functions are solutions of linear integral equations of special form. The spectrum of is a multiple infinite product of the spectra of atomic functions. dilated by the argument. Constructed generalized series has fast convergence. This property is confirmed by the presented truncation error bound formula and the results of a numerical experiment.

About the authors

K. A. Budunova

Kotelnikov Institute of Radio Engineering and Electronics of RAS

Author for correspondence.
Email: 1917schw@mail.ru
Russian Federation, 11-7, Mokhovaya street, Moscow, 125009

V. F. Kravchenko

Kotelnikov Institute of Radio Engineering and Electronics of RAS; Scientific and Technological Centre of Unique Instrumentation of RAS; Bauman Moscow State Technical University

Email: 1917schw@mail.ru
Russian Federation, 11-7, Mokhovaya street, Moscow, 125009; 15, Bytlerova street, Moscow, 117342; 5, 2-nd Baumanskaya, Moscow, 105005

V. I. Pustovoit

Scientific and Technological Centre of Unique Instrumentation of RAS; Bauman Moscow State Technical University

Email: 1917schw@mail.ru

Academician of the RAS

Russian Federation, 15, Bytlerova street, Moscow, 117342; 5, 2-nd Baumanskaya, Moscow, 105005

References

  1. Кравченко В.Ф., Рвачев В.Л. Алгебра логики, атомарные функции и вейвлеты в физических приложениях. М.: Физматлит, 2006.
  2. Кравченко В.Ф., Чуриков Д.В. Цифровая обработка сигналов атомарными функциями и вейвлетами. М.: Техносфера, 2018.
  3. Гуляев Ю.В., Кравченко В.Ф., Пустовойт В.И. // ДАН. 2007. Т.417. № 4. C. 476–482.
  4. Кравченко В.Ф., Кравченко О.В. Конструктивные методы алгебры логики, атомарных функций, вейвлетов, фракталов в физике и технике. М.: Техносфера, 2018.
  5. Кравченко В.Ф., Сафин А.Р. // Электромагн. волны и электрон. системы. 2008. Т. 13. № 12. С. 31.
  6. Budunova K.A., Konovalov Y.Y., Kravchenko O.V. Proc. Progress in Electromagnetics Research Symp. (PIERS). St Petersburg, 2017. N.Y.: IEEE, 2017. P. 1641.
  7. Будунова К.А., Кравченко В.Ф., Пустовойт В.И. // РЭ. 2018. Т. 63. № 9. С. 935–941.

Copyright (c) 2019 Russian academy of sciences

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies