Abstract
We introduce the concept of “covariant symbolic calculus” on real and complex symmetric domains, prove a general product formula for the link transform (generalized Berezin transform) between two such calculi, and describe a basic example (Toeplitz calculus) in more detail.
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References
J. Arazy, H. Upmeier, Invariant symbolic calculi and eigenvalues of invariant operators on symmetric domains, Proc. Lund 2000.
J. Arazy, H. Upmeier, Weyl calculus on rank 1 symmetric domains, Preprint (2000).
D. Borthwick, A. Lesniewski, H. Upmeier, Non-perturbative deformation quantization of Cartan domains, J. Func. Anal 113 (1993), 153–176.
G. van Dijk, M. Pevzner, Berezin kernels and tube domains, Preprint (1999).
J. Faraut, A. Korányi, Analysis on Symmetric Cones, Clarendon Press Oxford (1994).
S. Helgason, Groups and Geometric Analysis, Academic Press (1984).
O. Loos, Jordan Pairs, Springer Lect. Notes 460 (1975).
O. Loos, Bounded Symmetric Domains and Jordan Pairs, Univ. of California, Irvine (1977).
Y. Neretin, Matrix analogs of Beta-integral and Plancherel formula for Berezin kernel representations, Preprint (1999).
H. Upmeier, Symmetric Banach Manifolds and Jordan C*-Algebras, North Hol-land (1985).
A. Unterberger, H. Upmeier, The Berezin transform and invariant differential operators, Comm. Math. Phys. 164 (1994), 563–597.
G. Zhang, Berezin transform on real bounded symmetric domains, Preprint (1999).
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© 2003 Springer Basel AG
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Arazy, J., Upmeier, H. (2003). Covariant Symbolic Calculi on Real Symmetric Domains. In: Böttcher, A., Kaashoek, M.A., Lebre, A.B., dos Santos, A.F., Speck, FO. (eds) Singular Integral Operators, Factorization and Applications. Operator Theory: Advances and Applications, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8007-7_1
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DOI: https://doi.org/10.1007/978-3-0348-8007-7_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9401-2
Online ISBN: 978-3-0348-8007-7
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