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

This article is cited in 12 scientific papers (total in 12 papers)

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

Full text: PDF file (374 kB)
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English version:
Functional Analysis and Its Applications, 2000, 34:3, 197–207

Bibliographic databases:

UDC: 512.81
Received: 24.11.1998

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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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Yu. A. Neretin, “Matrix balls, radial analysis of Berezin kernels, and hypergeometric determinants”, Mosc. Math. J., 1:2 (2001), 157–220  mathnet  crossref  mathscinet  zmath  elib
    3. Borodin, A, “Infinite random matrices and ergodic measures”, Communications in Mathematical Physics, 223:1 (2001), 87  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Ben Said, S, “Weighted Bergman spaces on bounded symmetric domains”, Pacific Journal of Mathematics, 206:1 (2002), 39  crossref  mathscinet  isi  scopus
    5. Neretin, YA, “Hua-type integrals over unitary groups and over projective limits of unitary groups”, Duke Mathematical Journal, 114:2 (2002), 239  crossref  mathscinet  zmath  isi  scopus
    6. Neretin, YA, “Plancherel formula for Berezin deformation of L-2 on Riemannian symmetric space”, Journal of Functional Analysis, 189:2 (2002), 336  crossref  mathscinet  zmath  isi  scopus
    7. Yu. A. Neretin, “Rayleigh triangles and non-matrix interpolation of matrix beta integrals”, Sb. Math., 194:4 (2003), 515–540  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Olshanski, G, “The problem of harmonic analysis on the infinite-dimensional unitary group”, Journal of Functional Analysis, 205:2 (2003), 464  crossref  mathscinet  zmath  isi  scopus
    10. J. Math. Sci. (N. Y.), 141:4 (2007), 1452–1478  mathnet  crossref  mathscinet  zmath  elib
    11. Merigon S., Seppaenen H., “Branching laws for discrete Wallach points”, Journal of Functional Analysis, 258:10 (2010), 3241–3265  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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