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On approximation by Cesàro means of the Laguerre expansion and best approximation

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References

  1. R. Askey and I.I. Hirschman, Mean summability for ultrasperical polynomials. Math. Scand. 12 (1963), 167–177.

    MathSciNet  MATH  Google Scholar 

  2. R. Askey and S. Wainger, Mean convergence of expansions in Laguerre and Hermite series. Amer. J. Math. 87 (1965), 695–708.

    Article  MathSciNet  MATH  Google Scholar 

  3. 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.

    Article  MathSciNet  MATH  Google Scholar 

  4. 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.

  5. 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.

    Google Scholar 

  6. 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.

    MathSciNet  MATH  Google Scholar 

  7. 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.

    Article  MathSciNet  MATH  Google Scholar 

  8. 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).

  9. A. Erdélyi et al., Higher Transcendental Functions, vol. 2, McGraw Hill, New York, 1953.

    Google Scholar 

  10. E. Görlich and C. Markett, Mean Cesàro summability and operator norms for Laguerre expansions, (to appear).

  11. E. Görlich and C. Markett, Estimates for the norm of the Laguerre translation operator. Numerical Functional Analysis and Optimization, (in print).

  12. E. Görlich and C. Markett, On Abel-Poisson summation for Laguerre expansions, (in prepara- tion).

  13. 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.

    MathSciNet  Google Scholar 

  14. B. Muckenhoupt, Mean convergence ofHermite and Laguerre series II. Trans. Amer. Math. Soc. 147 (1970), 433–460.

    Article  MathSciNet  Google Scholar 

  15. G. Németh, On the L4-norm of orthogonal Laguerre polynomials. Studia Sci. Math. Hungar. 10 (1975), 243–246.

    MathSciNet  Google Scholar 

  16. E. Poiani, Mean Cesàro summability of Laguerre and Hermite Series. Trans. Amer. Math. Soc. 173 (1972), 1–31.

    MathSciNet  MATH  Google Scholar 

  17. R. L. Stens and M. Wehrens, Legendre transform methods and best algebraic approximation. Comment. Math. Prace Mat. 22 (1979). (in print).

  18. G. Szegö, Orthogonal Polynomials. 3rd ed., Amer. Math. Soc. Colloq. Publ. vol. 23, Providence, R.I., 1967.

    Google Scholar 

  19. G. N. Watson, A Treatise on the Theory of Bessel Functions. 2nd ed., Cambridge University Press, Cambridge, 1962.

    Google Scholar 

  20. A. Zygmund, Trigonometric Series I. 2nd ed., Cambridge University Press, Cambridge, 1959.

    Google Scholar 

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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

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