Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Fourier summation with kernels defined by Jacobi polynomials


Author: R. Lasser
Journal: Proc. Amer. Math. Soc. 114 (1992), 677-682
MSC: Primary 42A10
DOI: https://doi.org/10.1090/S0002-9939-1992-1072343-8
MathSciNet review: 1072343
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Trigonometric polynomial kernels defined by Jacobi polynomials are investigated. They generalize the classical Dirichlet kernel and the Fejér kernel. The asymptotic behavior of the corresponding Fourier summation obtained is leading to optimal kernels.


References [Enhancements On Off] (What's this?)

  • [1] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover Publ., New York, 1972.
  • [2] R. Askey, Jacobi summability, J. Approx. Theory 5 (1972), 387-392. MR 0336206 (49:982)
  • [3] -, Orthogonal polynomials and special functions, SIAM, Philadelphia, PA, 1975.
  • [4] P L. Butzer and R. J. Nessel, Fourier analysis and approximation. I, Birkhäuser, Basel, 1971. MR 0510857 (58:23312)
  • [5] G. Gasper, Positive sums of the classical orthogonal polynomials, SIAM J. Math. Anal. 8 (1977), 423-447. MR 0432946 (55:5925)
  • [6] E. M. Stein and A. Zygmund, On the boundary behavior of harmonic functions, Orthogonal Expansions and Continuous Analogues (D. Haimo, ed.), Southern Illinois Univ. Press, Carbondale, IL, 1968, pp. 127-141. MR 0234001 (38:2322)
  • [7] G. Szegö, Orthogonal polynomials, Amer. Math. Soc., New York, 1951.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A10

Retrieve articles in all journals with MSC: 42A10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1072343-8
Keywords: Fourier approximation, Jacobi polynomials
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society