TY - JOUR

T1 - To recovering of continuous function by sequences of its Fejér sums values at the given set of points

AU - Kachurovskii, Alexander

AU - Podvigin, Ivan

N1 - Funding Information:
The work was carried out in the framework of the State Contract of the Sobolev Institute of Mathematics (Project 0314-2019-0005)
Publisher Copyright:
© 2020 Proceedings of the International Geometry Center. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/10/13

Y1 - 2020/10/13

N2 - It is shown that a continuous 2p-periodic function is uniquely recovered (on the whole real line) by sequences of its Fejér sums values at the given finite set of points if and only if there exist two of these points with the distance between them incommensurable with p. And that full sets of Fejér integrals at any two different points always uniquely recover continuous absolutely Lebesgue integrable on the real line function. Wherein known sequence of Fejér sums values at a fixed single point x ∈ R and full set of Fejér integrals at this point determines uniquely a function only in the class of continuous functions with an even shift by x.

AB - It is shown that a continuous 2p-periodic function is uniquely recovered (on the whole real line) by sequences of its Fejér sums values at the given finite set of points if and only if there exist two of these points with the distance between them incommensurable with p. And that full sets of Fejér integrals at any two different points always uniquely recover continuous absolutely Lebesgue integrable on the real line function. Wherein known sequence of Fejér sums values at a fixed single point x ∈ R and full set of Fejér integrals at this point determines uniquely a function only in the class of continuous functions with an even shift by x.

KW - Continuous 2p-periodic functions

KW - Continuous absolutely Lebesgue integrable on the real line functions

KW - Fejér integrals

KW - Fejér sums

KW - Uniquely recovering

UR - http://www.scopus.com/inward/record.url?scp=85095877095&partnerID=8YFLogxK

U2 - 10.15673/TMGC.V13I3.1757

DO - 10.15673/TMGC.V13I3.1757

M3 - Article

AN - SCOPUS:85095877095

VL - 13

SP - 1

EP - 9

JO - Proceedings of the International Geometry Center

JF - Proceedings of the International Geometry Center

SN - 2072-9812

IS - 3

ER -