Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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To recovering of continuous function by its sequences of Fejer sums at given set of points

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Александр Григорьевич Качуровский
http://orcid.org/0000-0002-2747-2660
Иван Викторович Подвигин

Abstract

It is shown that continuous 2π-periodical function is uniquely recovered (on the whole real line) by its sequences of Fejer sums at the given finite set of points if and only if there exist two of these points with the distance between them incommensurable with π. And that full sets of Fejer integrals at any two different points always uniquely recover continuous absolutely Lebesgue integrable on the real line
function.
Wherein known sequence of Fejer sums at a single point neither full set of Fejer integrals at a single point could ever recover uniquely any of these continuous functions.

Keywords:
Fejer sums, continuous 2π-periodic functions, Fejer integrals, continuous absolutely Lebesgue integrable on the real line functions, uniquely recovering

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How to Cite
Качуровский, А., & Подвигин, И. (2020). To recovering of continuous function by its sequences of Fejer sums at given set of points. Proceedings of the International Geometry Center, 13(3), 1-9. https://doi.org/10.15673/tmgc.v13i3.1757
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Papers
Author Biographies

Александр Григорьевич Качуровский

Sobolev Institute of Mathematics, Novosibirsk, Russia

Иван Викторович Подвигин

Sobolev Institute of Mathematics; Novosibirsk State University; Novosibirsk, Russia