On the Basis Property of the System of Exponentials and Trigonometric Systems of Sine and Cosine Functions in Weighted Grand Lebesgue Spaces.

Autor: Ismailov, M. I., Aliyarova, I. F.
Zdroj: Moscow University Mathematics Bulletin; Apr2024, Vol. 79 Issue 2, p85-97, 13p
Abstrakt: The paper is focused on the basis property of the system of exponentials and trigonometric systems of sine and cosine functions in a separable subspace of the weighted grand Lebesgue space generated by the shift operator. In this paper, with the help of the shift operator, a separable subspace of the weighted space of the grand Lebesgue space is defined. The density in of the set of infinitely differentiable functions that are finite on is studied. It is proved that if the weight function satisfies the Mackenhoupt condition, then the system of exponentials forms a basis in , and trigonometric systems of sine and cosine functions form bases in . [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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