Estimates of generalized Lebesgue constants of partial Fourier-Jacobi sums

S.V. Goncharov (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-8071-8746
V.P. Motornyi (Oles Honchar Dnipropetrovsk National University)

Abstract


We obtain, in some cases, estimates of generalized Lebesgue constants of Fourier-Jacobi sums in $$$L_{p,w}$$$ spaces.

References


Badkov V.M. "On approximation of functions by Fourier-Jacobi sums", Dokl. AN SSSR, 1966; 167(4): pp. 731-734. (in Russian)

Badkov V.M. "Approximation of functions by partial sums of Fourier-Jacobi series in generalized Jacobi polynomials", Matem. zametki, 1968; 3(6): pp. 671-682. (in Russian) doi:10.1007/BF01110601

Badkov V.M. "Estimates of Lebesgue functions and remainder of Fourier-Jacobi series", Siberian Math. J., 1968; 9(6): pp. 1263-1283. (in Russian) doi:10.1007/BF02196447

Badkov V.M. "Approximative properties of Fourier series in orthogonal polynomials", Uspekhi matem. nauk, 1978; 33(4): pp. 51-106. (in Russian) doi:10.1070/RM1978v033n04ABEH002493

Goncharov S.V., Motornyi V.P. "On the mean convergence of Fourier-Jacobi series", Res. Math., 2008; 16: pp. 49-55. (in Russian)

Kazakova N.M. "On orders of Lebesgue constants of Fourier-Jacobi sums in $$$L^r_{\rho}$$$ spaces", Depon. in VINITI, Sverdlovsk, 1981; 54 p. (in Russian)

Motornyi V.P. "On mean convergence of Fourier series by Legendre polynomials", Dokl. AN SSSR, 1972; 204(4): pp. 788-790. (in Russian)

Motornyi V.P. "On mean convergence of Fourier series by Legendre polynomials", Izv. AN SSSR. Ser. Matematika, 1973; 37(1): pp. 135-147. (in Russian) doi:10.1070/IM1973v007n01ABEH001929

Motornyi V.P. "Approximation of functions by algebraic polynomials in $$$L_p$$$ metric", Izv. AN SSSR. Ser.: Matematika, 1971; 35(4): pp. 874-899. (in Russian) doi:10.1070/IM1971v005n04ABEH001122

Motornyi V.P. "Mean approximation of functions by Fourier-Legendre sums", Dokl. AN SSSR, 1981; 259(1): pp. 39-42. (in Russian)

Szego G. Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. vol. XXIII, Amer. Math. Soc, New York, 1959; Russian transl.: GIFML, Moscow, 1962.

Khodak L.B. "On convergence of Fourier-Jacobi series in integral metric", Depon. in Ukr. NIINTI, Dnipropetrovsk, 1979. (in Russian)

Khodak L.B. "Mean convergence of Fourier series by Jacobi polynomials", Dokl. AN USSR. Ser. A, 1982; 8: pp. 28-31. (in Russian)

Cartwright D.I. "Lebesgue constant for Jacobi expansions", Proc. Amer. Math. Soc., 1983; 87(3): pp. 427-433. doi:10.1090/S0002-9939-1983-0684632-1

Muckenhoupt B. "Mean convergence of Jacobi series", Proc. Amer. Math. Soc., 1969; 23(2): pp. 306-310. doi:10.2307/2037162

Newman J., Rudin W. "Mean convergence of orthogonal series", Proc. Amer. Math. Soc., 1952; 3(2): pp. 219-222. doi:10.2307/2032262

Pollard H. "The mean convergence of orthogonal series. I", Trans. Amer. Math. Soc., 1947; 62(3): pp. 387-403. doi:10.2307/1990463

Pollard H. "The mean convergence of orthogonal series. II", Trans. Amer. Math. Soc., 1948; 63(2): pp. 355-367. doi:10.2307/1990435

Pollard H. "The mean convergence of orthogonal series. III", Duke Math. J., 1949; 16(1): pp. 189-191. doi:10.1215/S0012-7094-49-01619-1

Wing G.M. "The mean convergence of orthogonal series", Amer. J. Math., 1950; 72(4): pp. 792-808. doi:10.2307/2372296




DOI: https://doi.org/10.15421/240807

  

Refbacks

  • There are currently no refbacks.


Copyright (c) 2008 S.V. Goncharov, V.P. Motornyi

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in

More►


ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
DNU