Lacunary interpolation by antiperiodic trigonometric polynomials

被引：49

作者：

Delvos, FJ ^{[1
]}

Knoche, L ^{[1
]}

机构：

[1] Univ Gesamthsch Siegen, Lehrstuhl Math 1, D-57068 Siegen, Germany

来源：

BIT | 1999年 / 39卷 / 03期

关键词：

lacunary interpolation; trigonometric interpolation; antiperiodic trigonometric interpolation;

D O I：

10.1023/A:1022314518264

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial T exist which satisfies T(x(k)) = a(k), (DT)-T-m(x(k)) = b(k), 0 less than or equal to k less than or equal to n - 1, where x(k), = k pi/n is a nodal set, a(k) and b(k) are prescribed complex numbers, D = d/dx and m is an element of N. Results obtained by several authors for the periodic case are extended to the antiperiodic case. In particular solvability is established when n as well as m are even. In this case a periodic solution does not exist.

引用

页码：439 / 450

页数：12