The Classes N(X) and RPD(X) : Integral Representations

  • J. H. Wells
  • L. R. Williams
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete Band 84 book series (MATHE2, volume 84)

Abstract

This chapter continues the study of radial positive definite functions and functions of negative type begun in the preceding chapter. Following methods introduced by Schoenberg [79,80,81] and recently refined by Bretagnolle, Dacunha Castelle, and Krivine [11], and Kuelbs [52], we are going to present characterizations of the classes RPD(X) and N(X) when X is one of the spaces ℝ n or L p (n = 1,2, … ; 0 < p ≤ ∞ ).

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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • J. H. Wells
    • 1
  • L. R. Williams
    • 2
  1. 1.University of KentuckyLexingtonUSA
  2. 2.Louisiana State UniversityBaton RougeUSA

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