Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Uniform Convergence of Expansions in Root Functions of a Differential Operator with Integral Boundary Conditions

Uniform Convergence of Expansions in Root Functions of a Differential Operator with Integral... for a second-order ordinary differential operator with integral boundary conditions on an interval of the real line, we derive conditions for the uniform convergence of the spectral expansion of a function in a series in the system of eigenfunctions and associated functions of the operator. We obtain estimates of the rate of convergence of the series and the rate of equiconvergence of such an expansion of a function and its expansion in the trigonometric Fourier series. We also study the uniform convergence of the expansion of a function in the biorthogonal system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Uniform Convergence of Expansions in Root Functions of a Differential Operator with Integral Boundary Conditions

Differential Equations , Volume 55 (4) – May 17, 2019

Loading next page...
 
/lp/springer-journals/uniform-convergence-of-expansions-in-root-functions-of-a-differential-dgKuIivf0c

References (33)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266119040049
Publisher site
See Article on Publisher Site

Abstract

for a second-order ordinary differential operator with integral boundary conditions on an interval of the real line, we derive conditions for the uniform convergence of the spectral expansion of a function in a series in the system of eigenfunctions and associated functions of the operator. We obtain estimates of the rate of convergence of the series and the rate of equiconvergence of such an expansion of a function and its expansion in the trigonometric Fourier series. We also study the uniform convergence of the expansion of a function in the biorthogonal system.

Journal

Differential EquationsSpringer Journals

Published: May 17, 2019

There are no references for this article.