Über die Konvergenz der ( C , 1 ) -Mittel von Fourier-Laguerre-Reihen

Dieter Ernst

Compositio Mathematica (1969)

  • Volume: 21, Issue: 1, page 81-101
  • ISSN: 0010-437X

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Ernst, Dieter. "Über die Konvergenz der $(C, 1)$-Mittel von Fourier-Laguerre-Reihen." Compositio Mathematica 21.1 (1969): 81-101. <http://eudml.org/doc/88999>.

@article{Ernst1969,
author = {Ernst, Dieter},
journal = {Compositio Mathematica},
keywords = {approximation and series expansion},
language = {ger},
number = {1},
pages = {81-101},
publisher = {Wolters-Noordhoff Publishing},
title = {Über die Konvergenz der $(C, 1)$-Mittel von Fourier-Laguerre-Reihen},
url = {http://eudml.org/doc/88999},
volume = {21},
year = {1969},
}

TY - JOUR
AU - Ernst, Dieter
TI - Über die Konvergenz der $(C, 1)$-Mittel von Fourier-Laguerre-Reihen
JO - Compositio Mathematica
PY - 1969
PB - Wolters-Noordhoff Publishing
VL - 21
IS - 1
SP - 81
EP - 101
LA - ger
KW - approximation and series expansion
UR - http://eudml.org/doc/88999
ER -

References

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  1. R. Askey- S. Wainger [1, a] Mean convergence of expansions in Laguerre and Hermite series. Amer. Journ. of Math.87, 695-708 (1965). Zbl0125.31301MR182834
  2. R. Askey [1, b] Norm inequalities for some orthogonal series. Bull. Amer. Math. Soc.72, 808-823 (1966). Zbl0173.06703MR198114
  3. R.C. Buck [2] Studies in Modern Math. M. H. Stone: A Generalized Weierstraß Approximation Theorem. Prentice-Hall, Inc.1962. Zbl0147.11702
  4. P.L. Butzer [3] Halbgruppen von linearen Operatoren und das Darstellungs- und Umkehr-problem für Laplace-Transformationen. Math. Ann.134, 154 —166 (1957). Zbl0078.28402
  5. R.C. Campbell [4] Généralisation de la formule de Féjèr pour les séries des polynomes usuels. Ann. Sei. Ecole Norm. Sup. (3), 71, 389-491 (1954). Zbl0057.05202
  6. W.B. Caton- E. Hille [5] Laguerre polynomials and Laplace integrals. Duke Math. J.12, 217-242 (1945). Zbl0060.25303MR12166
  7. A.G. Dominguez [6] Condiciones necesarias y suficientes para que una funcion sea una integral de Laplace. Rev. Unión Mat. Argentina2, 1— 9 (1938). 
  8. Erdélyi-Magnus-Oberhettinger-Tricomi [7] Higher Transcendental Functions, Vol. II. McGraw-Hill1953. Zbl0051.30303
  9. E. Kogbetliantz [8, a] Recherches sur la sommabilité des séries d'Hermite. Ann. Sci. Ecole Norm. Sup. (3), 49137-221 (1932). Zbl0005.15701MR1509321JFM58.0286.02
  10. [8, b] Sur les moyennes arithmétiques des séries-noyaux des développements en series d'Hermite et de Laguerre et sur celles de ces séries-noyaux derivées terme à terme. Journ. Math. and Phys.15, 37-99 (1935). Zbl0012.06503JFM61.0291.02
  11. G. Szegö [9, a] Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. Vol. 23, New York1959. Zbl0089.27501
  12. [9, b] Zur Theorie der Laguerre'schen Polynome I. Math. Zeitschr.25, 87-115 (1926). JFM52.0280.04
  13. G.N. Watson [10] A Treatise on the Theory of Bessel-Functions. Cambridge1962. JFM50.0264.01

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