Total positivity, spherical series, and hypergeometric functions of matrix argument

Kenneth I. Gross, Donald Richards

Research output: Contribution to journalArticle

92 Citations (Scopus)

Abstract

Given a totally positive function K of two real variables, is there a method for establishing the total positivity of K in an "obvious" fashion? In the case in which K(x, y) = f(xy), where f is real-analytic in a neighborhood of zero, we obtain integral representations for the determinants which define the total positivity of K. The total positivity of K then follows immediately from positivity of the integrands. In particular, we analyze the total positivity of classical hypergeometric functions by these methods. The central theme of this work is the circle of ideas that relates total positivity to "spherical series" on the symmetric space GL(n, C) U(n), and classical hypergeometric functions to hypergeometric functions of matrix argument.

Original languageEnglish (US)
Pages (from-to)224-246
Number of pages23
JournalJournal of Approximation Theory
Volume59
Issue number2
DOIs
StatePublished - Jan 1 1989

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Total Positivity
Hypergeometric Functions
Series
Real variables
Integrand
Symmetric Spaces
Positivity
Integral Representation
Immediately
Determinant
Circle
Zero

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

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Total positivity, spherical series, and hypergeometric functions of matrix argument. / Gross, Kenneth I.; Richards, Donald.

In: Journal of Approximation Theory, Vol. 59, No. 2, 01.01.1989, p. 224-246.

Research output: Contribution to journalArticle

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