On Fourier Series in Generalized Eigenfunctions of a Discrete Sturm-Liouville Operator

被引：2

作者：

Osilenker, B. P. ^{[1
]}

机构：

[1] Moscow State Univ Civil Engn, Moscow, Russia

来源：

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2018年 / 52卷 / 02期

关键词：

Fourier series; discrete operator; Sturm-Liouville operator; eigenfunctions; orthogonal polynomials; semicontinuous summation methods; generalized heat equation; Jacobi polynomials; Pollaczek polynomials; loaded Gegenbauer polynomials;

D O I：

10.1007/s10688-018-0223-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For semicontinuous summation methods generated by I > = {lambda (n) (h)} (n = 0, 1, 2,...; h > 0) of Fourier series in eigenfunctions of a discrete Sturm-Liouville operator of class B, some results on the uniform a.e. behavior of I >-means are obtained. The results are based on strong- and weak-type estimates of maximal functions. As a consequence, some statements on the behavior of the summation methods generated by the exponential means lambda (n) (h) = exp(-u(alpha)(n)h) are obtained. An application to a generalized heat equation is given.

引用

页码：154 / 157

页数：4

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