On the Faraut-Koranyi hypergeometric functions in rank two

Miroslav Engliš[1]; Genkai Zhang

  • [1] Academy of Sciences, Mathematics Institute, Zitna 25, 11567 Prague 1 (Czech Republic), Göteborgs Universitet, Chalmers tekniska högskola, 41296 Göteborg (Sweden)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 6, page 1855-1875
  • ISSN: 0373-0956

Abstract

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We give a complete description of the boundary behaviour of the generalized hypergeometric functions, introduced by Faraut and Koranyi, on Cartan domains of rank 2. The main tool is a new integral representation for some spherical polynomials, which may be of independent interest.

How to cite

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Engliš, Miroslav, and Zhang, Genkai. "On the Faraut-Koranyi hypergeometric functions in rank two." Annales de l’institut Fourier 54.6 (2004): 1855-1875. <http://eudml.org/doc/116162>.

@article{Engliš2004,
abstract = {We give a complete description of the boundary behaviour of the generalized hypergeometric functions, introduced by Faraut and Koranyi, on Cartan domains of rank 2. The main tool is a new integral representation for some spherical polynomials, which may be of independent interest.},
affiliation = {Academy of Sciences, Mathematics Institute, Zitna 25, 11567 Prague 1 (Czech Republic), Göteborgs Universitet, Chalmers tekniska högskola, 41296 Göteborg (Sweden)},
author = {Engliš, Miroslav, Zhang, Genkai},
journal = {Annales de l’institut Fourier},
keywords = {Cartan domain; hypergeometric function; partition; spherical polynomial; Jack polynomial; hypergeometric functions; Jack polynomials; integral representation},
language = {eng},
number = {6},
pages = {1855-1875},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the Faraut-Koranyi hypergeometric functions in rank two},
url = {http://eudml.org/doc/116162},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Engliš, Miroslav
AU - Zhang, Genkai
TI - On the Faraut-Koranyi hypergeometric functions in rank two
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 6
SP - 1855
EP - 1875
AB - We give a complete description of the boundary behaviour of the generalized hypergeometric functions, introduced by Faraut and Koranyi, on Cartan domains of rank 2. The main tool is a new integral representation for some spherical polynomials, which may be of independent interest.
LA - eng
KW - Cartan domain; hypergeometric function; partition; spherical polynomial; Jack polynomial; hypergeometric functions; Jack polynomials; integral representation
UR - http://eudml.org/doc/116162
ER -

References

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  11. H. Upmeier, Toeplitz operators on bounded symmetric domains, Trans. Amer. Math. Soc 280 (1983), 221-237 Zbl0527.47019MR712257
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  13. K. Zhu, Holomorphic Besov spaces on bounded symmetric domains, Quart. J. Math. Oxford 46 (1995), 239-256 Zbl0837.32013MR1333834
  14. M. Engliš, Compact Toeplitz operators via the Berezin transform on bounded symmetric domains, Integral Eq. Oper. Theory (Erratum Ibid) 34 (1999), 500-501 Zbl0936.47014MR1702236

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