Arazy, Upmeier: Weyl calculus for complex and real symmetric domains

Arazy, Jonathan and 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 Serie 9 13 (2002), fasc. n.3-4, p. 165-181, (English)
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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.

Referenze Bibliografiche

[1] J. Arazy - H. Upmeier, 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] J. Arazy - H. Upmeier, 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] G. van Dijk - M. Pevzner, Berezin kernels and tube domains. J. Funct. Anal., to appear. | fulltext (doi) | MR 1821696 | Zbl 0970.43003

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

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

[6] S. Helgason, Groups and Geometric Analysis. Academic Press, New York 1984. | MR 754767 | Zbl 0543.58001

[7] O. Loos, Bounded Symmetric Domains and Jordan Pairs. Univ. of California, Irvine 1977.

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

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

[10] A. Unterberger - J. Unterberger, La série discrète de $SL(2,\mathbb{R})$ et les opérateurs pseudo-différentiels sur une demi-droite. Ann. Sci. Ec. Norm. Sup., 17, 1984, 83-116. | fulltext EuDML | fulltext mini-dml | MR 744069 | Zbl 0549.35119

[11] A. Unterberger - J. Unterberger, A quantization of the Cartan domain $BD$$I(q = 2)$ and operators on the light cone. J. Funct. Anal., 72, 1987, 279-319. | fulltext (doi) | MR 886815 | Zbl 0632.58033

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

[13] H. Upmeier, Symmetric Banach Manifolds and Jordan $C^{∗}$-Algebras. North Holland 1985. | MR 776786 | Zbl 0561.46032

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

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

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Referenze Bibliografiche