Journal
JOURNAL OF APPROXIMATION THEORY
Volume 117, Issue 2, Pages 207-228Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jath.2002.3697
Keywords
Fourier-Jacobi series; uniform convergence; generalized bounded variation
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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).
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