Weyl calculus for complex and real symmetric domains
Arazy, Jonathan ; Upmeier, Harald
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002), p. 165-181 / Harvested from Biblioteca Digitale Italiana di Matematica
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We define the Weyl functional calculus for real and complex symmetric domains, and compute the associated Weyl transform in the rank 1 case.

Publié le : 2002-12-01
@article{RLIN_2002_9_13_3-4_165_0,
     author = {Jonathan Arazy and Harald Upmeier},
     title = {Weyl calculus for complex and real symmetric domains},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {13},
     year = {2002},
     pages = {165-181},
     zbl = {1150.43302},
     mrnumber = {1984098},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2002_9_13_3-4_165_0}
}

Arazy, Jonathan; Upmeier, Harald. Weyl calculus for complex and real symmetric domains. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002) pp. 165-181. http://gdmltest.u-ga.fr/item/RLIN_2002_9_13_3-4_165_0/

[1] Arazy, J. - Upmeier, H., Invariant symbolic calculi and eigenvalues of invariant operators on symmetric domains. Conference on Function Spaces, Interpolation Theory, and related topics in honour of Jaak Peetre on his 65th birthday. University of Lund, Sweden, August 17-22 2000. | Zbl 1027.32020

[2] Arazy, J. - Upmeier, H., Covariant symbolic calculi on real symmetric domains. International Workshop on Operator Theory and Applications (Faro, September 12-15 2000). IWOTA-Portugal 2000. | Zbl 1034.46071

[3] Van Dijk, G. - Pevzner, M., Berezin kernels and tube domains. J. Funct. Anal., to appear. | MR 1821696 | Zbl 0970.43003

[4] Faraut, J. - Korányi, A., Analysis on Symmetric Cones. Clarendon Press, Oxford 1994. | MR 1446489 | Zbl 0841.43002

[5] Folland, G., Harmonic Analysis in Phase Space. Princeton Univ. Press, 1989. | MR 983366 | Zbl 0682.43001

[6] Helgason, S., Groups and Geometric Analysis. Academic Press, New York1984. | MR 754767 | Zbl 0543.58001

[7] Loos, O., Bounded Symmetric Domains and Jordan Pairs. Univ. of California, Irvine1977.

[8] Magnus, W. - Oberhettinger, F. - Soni, R.P., Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag, New York 1966. | MR 232968 | Zbl 0143.08502

[9] Neretin, Y., Matrix analogs of Beta-integral and Plancherel formula for Berezin kernel representations. Preprint.

[10] Unterberger, A. - Unterberger, J., La série discrète de S⁢L⁢2,R et les opérateurs pseudo-différentiels sur une demi-droite. Ann. Sci. Ec. Norm. Sup., 17, 1984, 83-116. | MR 744069 | Zbl 0549.35119

[11] Unterberger, A. - Unterberger, J., A quantization of the Cartan domain B⁢DIq=2 and operators on the light cone. J. Funct. Anal., 72, 1987, 279-319. | MR 886815 | Zbl 0632.58033

[12] Unterberger, A. - Upmeier, H., The Berezin transform and invariant differential operators. Comm. Math. Phys., 164, 1994, 563-597. | MR 1291245 | Zbl 0843.32019

[13] Upmeier, H., Symmetric Banach Manifolds and Jordan C∗-Algebras. North Holland1985. | MR 776786 | Zbl 0561.46032

[14] Upmeier, H., Weyl quantization of symmetric spaces: hyperbolic matrix domains. J. Funct. Anal., 96, 1991, 297-330. | MR 1101260 | Zbl 0736.47014

[15] Zhang, G., Berezin transform on real bounded symmetric domains. Preprint. | MR 1837258 | Zbl 0965.22015