Abstract:
In this paper we compute the radial parts of the projections of orbital measures for the compact Lie groups of B, C, and D type, extending previous results obtained for the case of the unitary group by Olshanski and Faraut. Applying the method of Faraut, we show that the radial part of the projection of an orbital measure is expressed in terms of a B-spline with knots
located symmetrically with respect to zero.
Keywords:
orbital measures, B-splines, divided differences, Harish-Chandra–Itzykson–Zuber integral.
Citation:
D. Zubov, “Projections of orbital measures for classical Lie groups”, Funktsional. Anal. i Prilozhen., 50:3 (2016), 76–81; Funct. Anal. Appl., 50:3 (2016), 228–232
\Bibitem{Zub16}
\by D.~Zubov
\paper Projections of orbital measures for classical Lie groups
\jour Funktsional. Anal. i Prilozhen.
\yr 2016
\vol 50
\issue 3
\pages 76--81
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\transl
\jour Funct. Anal. Appl.
\yr 2016
\vol 50
\issue 3
\pages 228--232
\crossref{https://doi.org/10.1007/s10688-016-0151-2}
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Linking options:
https://www.mathnet.ru/eng/faa3250
https://doi.org/10.4213/faa3250
https://www.mathnet.ru/eng/faa/v50/i3/p76
This publication is cited in the following 3 articles:
G. I. Olshanski, “Characters of classical groups, Schur-type functions and discrete splines”, Sb. Math., 214:11 (2023), 1585–1626
P. J. Forrester, J. R. Ipsen, D.-Zh. Liu, L. Zhang, “Orthogonal and symplectic harish-chandra integrals and matrix product ensembles”, Random Matrices-Theor. Appl., 8:4 (2019), 1950015
Jacques Faraut, “Horn's problem and Fourier analysis”, Tunisian J. Math., 1:4 (2019), 585
Citation in format AMSBIB
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