Weyl calculus for complex and real symmetric domains
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 3-4, pp. 165-181.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We define the Weyl functional calculus for real and complex symmetric domains, and compute the associated Weyl transform in the rank 1 case.
@article{RLIN_2002_9_13_3-4_a0,
     author = {Arazy, Jonathan and Upmeier, Harald},
     title = {Weyl calculus for complex and real symmetric domains},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {165--181},
     publisher = {mathdoc},
     volume = {Ser. 9, 13},
     number = {3-4},
     year = {2002},
     zbl = {1150.43302},
     mrnumber = {1821696},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_3-4_a0/}
}
TY  - JOUR
AU  - Arazy, Jonathan
AU  - Upmeier, Harald
TI  - Weyl calculus for complex and real symmetric domains
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 2002
SP  - 165
EP  - 181
VL  - 13
IS  - 3-4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_3-4_a0/
LA  - en
ID  - RLIN_2002_9_13_3-4_a0
ER  - 
%0 Journal Article
%A Arazy, Jonathan
%A Upmeier, Harald
%T Weyl calculus for complex and real symmetric domains
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 2002
%P 165-181
%V 13
%N 3-4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_3-4_a0/
%G en
%F RLIN_2002_9_13_3-4_a0
Arazy, Jonathan; Upmeier, Harald. Weyl calculus for complex and real symmetric domains. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 3-4, pp. 165-181. http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_3-4_a0/

[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

[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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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. | DOI | MR | Zbl

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

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

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

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