Abstract
A summation method is constructed for the Fourier-Jacobi series, which has properties similar to the properties of the de la Vallée-Poussin methods of summation of the Fourier series by the trigonometric system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. S. Kashin and A.A. Saakyan,Orthogonal Series [in Russian], Nauka, Moscow (1984)
G. Szegö,Orthogonal Polynomials, American Mathematical Society, Colloquium Publications, Vol. 23, Providence, R.I. (1975).
K. V. Runovskii, “Direct and inverse theorems on the approximation by ‘an angle’ by algebraic polynomials,” in:Extremal Problems, Functional Analysis, and Applications [in Russian], Moscow University, Moscow (1988), pp. 50–53.
M. K. Potapov, “Approximations by algebraic polynomials in the integral metrics with Jacobi weights,”Vestn. Mosk. Univ., Ser. Mat. Mekh., No. 4 (1983), pp, 43–52.
A. F. Timan,Theory of Approximation of Functions of a Real Variable, Pergamon Press, Oxford-London-New York-Paris (1963).
A. Zygmund,Trigonometric Series, Vol. 1, Cambridge University Press, Cambridge (1959).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 676–680, May, 1993.
Rights and permissions
About this article
Cite this article
Runovskii, K.V. A method of summation of the Fourier-Jacobi series. Ukr Math J 45, 739–744 (1993). https://doi.org/10.1007/BF01058209
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058209