To recovering of continuous function by its sequences of Fejer sums at given set of points

To recovering of continuous function by its sequences of Fejer sums at given set of points Full article

Journal

Proceedings of the International Geometry Center
ISSN: 2072-9812 , E-ISSN: 2409-8906

Output data

Year: 2020, Volume: 13, Number: 3, Pages: 1-9 Pages count : 9 DOI: 10.15673/tmgc.v13i3.1757

Tags

Continuous 2p-periodic functions; Continuous absolutely Lebesgue integrable on the real line functions; Fejér integrals; Fejér sums; Uniquely recovering

Authors

Kachurovskii A. ¹ , Podvigin I. ^1,2

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, Russia
2	Novosibirsk State University, Novosibirsk, Russia

It is shown that a continuous 2π-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 π. 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 P 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.

Kachurovskii A. , Podvigin I.
To recovering of continuous function by its sequences of Fejer sums at given set of points
Proceedings of the International Geometry Center. 2020. V.13. N3. P.1-9. DOI: 10.15673/tmgc.v13i3.1757 Scopus OpenAlex

Scopus:	2-s2.0-85095877095
OpenAlex:	W3124037379

Пока нет цитирований