Uniform convergence of Fourier---Jacobi series

  • Authors:

  • George Kvernadze

  • Affiliations:

  • Department of Mathematics, Weber State University, Ogden, Utah

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2002

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Abstract

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, Λ-variation, and the modulus of variation of a function.