Uniform convergence of Fourier-Jacobi series

[摘要] Necessary and sufficient conditions which imply the uniform convergence of the Fourier-Jacobi series of a continuous function are obtained under an assumption that the Fourier-Jacobi series is convergent at the end points of the segment of orthogonality [-1, 1]. The conditions are in terms of the modulus of continuity, Lambda-variation, and the modulus of variation of a function. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-08-01

[关键词] Fourier-Jacobi series;uniform convergence;generalized bounded variation