References
R. Askey and I.I. Hirschman, Mean summability for ultrasperical polynomials. Math. Scand. 12 (1963), 167–177.
R. Askey and S. Wainger, Mean convergence of expansions in Laguerre and Hermite series. Amer. J. Math. 87 (1965), 695–708.
H. Berens, P. L. Butzer, and S. Pawelke, Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten. Publ. Res. Inst. Math. Sci. Ser. A 4 (1968), 201–268.
P. L. Butzer, R. J. Nessel, and W. Trebels, On summation processes of Fourier expansions in Banach spaces. II: Saturation theorems. Tôhoku Math. J. (2) 24 (1972) 551-569.
P. L. Butzer and K. Scherer, über die Fundamentalsätze der klassischen Approximationstheorie in abstrakten Räumen. In: P. L. Butzer and B. Sz.-Nagy (Eds.), Abstract Spaces and Approximation (Proc. Conf. Math. Res. Inst. Oberwolfach, Black Forest, 1968; ISNM 10), Birkhäuser, Basel-Stuttgart, 1969, 113–125.
P. L. Butzer and R. L. Stens, The operational properties of the Chebyshev transform. I: General properties. Funct. Approximatio Comment. Math. 5 (1977), 129–160.
P. L. Butzer and R. L. Stens, Chebyshev transform methods in the theory of best algebraic approximation. Abh. Math. Sem. Univ. Hamburg 45 (1976), 165–190.
P. L. Butzer, R. L. Stens, and M. Wehrens, Approximation by algebraic convolution integrals. In: Approximation Theory and Functional Analysis. (Proc. of the Conference held at Campinas, Brazil, August 1977; Ed. J. B. Prolla) North-Holland, Amsterdam-London, 1978. (in print).
A. Erdélyi et al., Higher Transcendental Functions, vol. 2, McGraw Hill, New York, 1953.
E. Görlich and C. Markett, Mean Cesàro summability and operator norms for Laguerre expansions, (to appear).
E. Görlich and C. Markett, Estimates for the norm of the Laguerre translation operator. Numerical Functional Analysis and Optimization, (in print).
E. Görlich and C. Markett, On Abel-Poisson summation for Laguerre expansions, (in prepara- tion).
E. Göruch, R. J. Nessel, and W. Trebels, Bernstein-type inequalities for families of multiplier operators in Banach spaces with Cesàro decompositions. II: Applications. Acta. Sci. Math. (Szeged) 36 (1974), 39–48.
B. Muckenhoupt, Mean convergence ofHermite and Laguerre series II. Trans. Amer. Math. Soc. 147 (1970), 433–460.
G. Németh, On the L4-norm of orthogonal Laguerre polynomials. Studia Sci. Math. Hungar. 10 (1975), 243–246.
E. Poiani, Mean Cesàro summability of Laguerre and Hermite Series. Trans. Amer. Math. Soc. 173 (1972), 1–31.
R. L. Stens and M. Wehrens, Legendre transform methods and best algebraic approximation. Comment. Math. Prace Mat. 22 (1979). (in print).
G. Szegö, Orthogonal Polynomials. 3rd ed., Amer. Math. Soc. Colloq. Publ. vol. 23, Providence, R.I., 1967.
G. N. Watson, A Treatise on the Theory of Bessel Functions. 2nd ed., Cambridge University Press, Cambridge, 1962.
A. Zygmund, Trigonometric Series I. 2nd ed., Cambridge University Press, Cambridge, 1959.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Görlich, E. On approximation by Cesàro means of the Laguerre expansion and best approximation. Results. Math. 2, 124–150 (1979). https://doi.org/10.1007/BF03322952
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322952