Log-convexity properties of Schur functions and generalized hypergeometric functions of matrix argument

Research output: Contribution to journalArticle

Abstract

We establish a positivity property for the difference of products of certain Schur functions, sλ(x), where λ varies over a fundamental Weyl chamber in ℝn and x belongs to the positive orthant in ℝn. Further, we generalize that result to the difference of certain products of arbitrary numbers of Schur functions. We also derive a log-convexity property of the generalized hypergeometric functions of two Hermitian matrix arguments, and we show how that result may be extended to derive higher-order log-convexity properties.

Original languageEnglish (US)
Pages (from-to)397-407
Number of pages11
JournalRamanujan Journal
Volume23
Issue number1
DOIs
StatePublished - Dec 1 2010

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Log-convexity
Generalized Hypergeometric Function
Schur Functions
Hermitian matrix
Positivity
Vary
Higher Order
Generalise
Arbitrary

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Log-convexity properties of Schur functions and generalized hypergeometric functions of matrix argument. / Richards, Donald.

In: Ramanujan Journal, Vol. 23, No. 1, 01.12.2010, p. 397-407.

Research output: Contribution to journalArticle

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