On the uniform convergence of the Fourier series for one spectral problem with a spectral parameter in a boundary condition. (10th November 2015)

• Record Type: Journal Article
• Authors: Kerimov, Nazim B.; Maris, Emir A.
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 9(2016:Jun. 15)
• Page Start: 2298
• Page End: 2309
• Publication Date: 2015-11-10
• Subjects: eigenvalues and eigenfunctions -- asymptotic formulae -- uniform convergence; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3640
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we investigate the uniform convergence of the Fourier series expansions in terms of eigenfunctions for the spectral problem − y ′′ + q ( x ) y = λy, 0 < x < 1, where λ is a spectral parameter, q ( x ) is a real‐valued continuous function on the interval [0, 1], and a 1, b 0, b 1, c 1, d 0, and d 1 are real constants that satisfy the conditions b 0 y ( 0 ) = d 0 y ′ ( 0 ), a 1 λ + b 1 y ( 1 ) = c 1 λ + d 1 y ′ ( 1 ), Copyright © 2015 John Wiley & Sons, Ltd.