Compact group actions, spherical bessel functions, and invariant random variables

Kenneth I. Gross, Donald Richards

Research output: Contribution to journalArticle

Abstract

The theory of compact group actions on locally compact abelian groups provides a unifying theory under which different invariance conditions studied in several contexts by a number of statisticians are subsumed as special cases. For example, Schoenberg's characterization of radially symmetric characteristic functions on Rn is extended to this general context and the integral representations are expressed in terms of the generalized spherical Bessel functions of Gross and Kunze. These same Bessel functions are also used to obtain a variant of the Lévy-Khinchine formula of Parthasarathy, Ranga Rao, and Varadhan appropriate to invariant distributions.

Original languageEnglish (US)
Pages (from-to)128-138
Number of pages11
JournalJournal of Multivariate Analysis
Volume21
Issue number1
DOIs
StatePublished - Jan 1 1987

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Bessel functions
Spherical Functions
Compact Group
Bessel Functions
Group Action
Random variables
Random variable
Invariant Distribution
Locally Compact Abelian Group
Invariant
Symmetric Functions
Invariance
Characteristic Function
Gross
Integral Representation
Context
Characteristic function
Integral
Invariant distribution

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

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Compact group actions, spherical bessel functions, and invariant random variables. / Gross, Kenneth I.; Richards, Donald.

In: Journal of Multivariate Analysis, Vol. 21, No. 1, 01.01.1987, p. 128-138.

Research output: Contribution to journalArticle

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