Annali di Matematica Pura ed Applicata

, Volume 59, Issue 1, pp 285–318 | Cite as

Classes of biorthonormal systems

Second part
  • Jacob Steinberg


The (A)-summability and mean-convergence of Fourier series in terms of certain biorthonormal systems have been investigated.

The problem of completing a set of polynomials to a biothonormal system has been solved in the case of certain sets of type zero (Sheffer’s classification).


Fourier Series Biorthonormal System 
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  1. [1]
    R. Boas andC. Buck,Polynomial expansions of analytic functions, « Ergebnisse der Mathematik», Neue Folge. No. 19, 1958.Google Scholar
  2. [2]
    G. Doetsch,Handbuch der Laplace TRansformation, Band I, Birkhauser, Basel, 1950.Google Scholar
  3. [3]
    E. Goursat,Course d’Analyse, Tome III, Gauthier-Villars, Paris, 1956.Google Scholar
  4. [4]
    R. Paley andN. Wienier,Fourier transforms in the complex domain, « American Mathematical Society Colloquium Publications», Vol. XIX, 1934.Google Scholar
  5. [5]
    G. Pólia andG. Szegö,Aufgaben und Lehrsätze aus der Analysis, Erster Band, Springer, 1954.Google Scholar
  6. [6]
    E. Rainville,Special Functions, Macmillan, New York, 1960.Google Scholar
  7. [7]
    I. Sheffer,Some properties of polynomial sets of type zero, « Duke Mathematical Journal», Vol. 5. No. 3, 1939.Google Scholar
  8. [8]
    -- --,Note on Appell polynomials, « Bull. Am. Math. Soc.», Vol. 51, No. 10, 1945.Google Scholar
  9. [9]
    J. Steinberg,Classes of biorthonormal systems, « Annali di Matematica pura ed applicata», Serie IV, Tomo LII, 1960.Google Scholar
  10. [10]
    -- --,Functions almost all of whose moments vanish, « Bulletin of the Research Council of Israel», Vol. 8 F. No. 2, 1959.Google Scholar
  11. [11]
    -- --,Integral tranforms with two reproducing properties, « Bulletin of the Research Council of Israel», Vol. 8 F, No. 4, 1960.Google Scholar
  12. [12]
    G. Szegö,Orthogonal Polynomials, « Colloquium Publications of the American Mathematical Society», Vol. XXIII, 1959.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1962

Authors and Affiliations

  • Jacob Steinberg
    • 1
  1. 1.HaifaIsrael

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