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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 3, Pages 49–62 (Mi faa311)

On the Separation of Spectra in the Analysis of Berezin Kernels

Yu. A. Neretin

Moscow State Institute of Electronics and Mathematics

Abstract: The problem of restricting a highest weight representation of the group $\operatorname{U}(p,q)$ to the subgroup $\operatorname{O}(p,q)$ is considered. This restriction has an intricate spectrum that contains representations of different types. We construct a decomposition of this representation into reducible representations each of which has a single-type spectrum.
Some integrals over classical groups are also calculated; these integrals generalize those of Hua.

DOI: https://doi.org/10.4213/faa311

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English version:
Functional Analysis and Its Applications, 2000, 34:3, 197–207

Bibliographic databases:

UDC: 512.81

Citation: Yu. A. Neretin, “On the Separation of Spectra in the Analysis of Berezin Kernels”, Funktsional. Anal. i Prilozhen., 34:3 (2000), 49–62; Funct. Anal. Appl., 34:3 (2000), 197–207

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/faa311
• https://doi.org/10.4213/faa311
• http://mi.mathnet.ru/eng/faa/v34/i3/p49

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. A. Neretin, “Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces”, Sb. Math., 192:3 (2001), 403–432
2. Yu. A. Neretin, “Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants”, Mosc. Math. J., 1:2 (2001), 157–220
3. Borodin, A, “Infinite random matrices and ergodic measures”, Communications in Mathematical Physics, 223:1 (2001), 87
4. Ben Said, S, “Weighted Bergman spaces on bounded symmetric domains”, Pacific Journal of Mathematics, 206:1 (2002), 39
5. Neretin, YA, “Hua-type integrals over unitary groups and over projective limits of unitary groups”, Duke Mathematical Journal, 114:2 (2002), 239
6. Neretin, YA, “Plancherel formula for Berezin deformation of L-2 on Riemannian symmetric space”, Journal of Functional Analysis, 189:2 (2002), 336
7. Yu. A. Neretin, “Rayleigh triangles and non-matrix interpolation of matrix beta integrals”, Sb. Math., 194:4 (2003), 515–540
8. Yu. A. Neretin, “Beta functions of Bruhat–Tits buildings and deformation of $l^2$ on the set of $p$-adic lattices”, Sb. Math., 194:12 (2003), 1775–1805
9. Olshanski, G, “The problem of harmonic analysis on the infinite-dimensional unitary group”, Journal of Functional Analysis, 205:2 (2003), 464
10. J. Math. Sci. (N. Y.), 141:4 (2007), 1452–1478
11. Merigon S., Seppaenen H., “Branching laws for discrete Wallach points”, Journal of Functional Analysis, 258:10 (2010), 3241–3265
12. Krantz S., “Harmonic and Complex Analysis in Several Variables”, Harmonic and Complex Analysis in Several Variables, Springer Monographs in Mathematics, Springer, 2017, 1–424
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