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Matematicheskie Zametki, 2019, Volume 106, Issue 6, paper published in the English version journal
(Mi mzm12328)
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This article is cited in 3 scientific papers (total in 3 papers)
Papers published in the English version of the journal
Strictly Positive Definite Functions on the Space
of Infinite Diagonal Matrices
M. Rabaouiabc a Department of Mathematics and Statistics,
College of Science, King Faisal University,
P.O. Box 400 Al-Ahsa, 31982 Kingdom of Saudi Arabia
b Institut préparatoire aux études d'ingénieur de Nabeul,
Université de Carthage, Nabeul, 8000 Tunisie
c Laboratoire d'Analyse Mathématique et Applications LR11ES11, Faculté des Sciences de Tunis,
Université de Tunis El Manar, El Manar Tunis, 2092 Tunisie
Abstract:
In this paper, using a Bochner-type theorem,
we establish a characterization of strictly positive
definite functions on the topological direct limit
space
$\mathcal D_{_\infty}$
of real diagonal matrices relatively to the action
of the product group
$K_{_\infty}=U_{_\infty}\times
U_{_\infty}$,
where
$U_{_\infty}$
is the infinite dimensional
unitary group.
Keywords:
Olshanski spherical pairs, generalized Bochner theorem, strictly positive definite
functions.
Received: 28.01.2019 Revised: 28.01.2019
Citation:
M. Rabaoui, “Strictly Positive Definite Functions on the Space
of Infinite Diagonal Matrices”, Math. Notes, 106:6 (2019), 966–969
Linking options:
https://www.mathnet.ru/eng/mzm12328
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