Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

被引：15

作者：

Gorbachev, D. V. ^{[1
]}

Ivanov, V. I. ^{[1
]}

机构：

[1] Tula State Univ, Tula, Russia

来源：

SBORNIK MATHEMATICS | 2015年 / 206卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

Gauss and Markov quadrature formulae; entire function of exponential type; Sturm-Liouville problem; Jacobi transform; Jacobi functions and polynomials; EXTREMUM PROBLEM; JACOBI FUNCTIONS; FOURIER; INEQUALITIES;

D O I：

10.1070/SM2015v206n08ABEH004490

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given.

引用

页码：1087 / 1122

页数：36

共 39 条

[1]

Akhiezer N.I., 1965, MATH LEHRBUCHER MONO, VII

[2] On real Paley-Wiener theorems for certain integral transforms [J].