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Seminarium i matematik

Uniform continuity and Toeplitz quantization on C^n or bounded symmetric domains

Välkommen till föreläsningen i seminarieserien i matematik.

I will report some progress on Toeplitz quantization for the Bergman space over bounded symmetric domains or the Segal-Bargmann space of Gaussian square integrable entire functions. Asymptotic relations in Rieffel’s definition of deformation quantization are extended to classes of i.g. non-continuous and possibly unbounded operator symbols. In case of Ω = Cn and for the Segal-Bargmann space these results can be formulated within the Fock quantization algebra via an oscillation condition.

The resulting estimates are useful in the analysis of Toeplitz C∗-algebras and their irreducible representations after a reduction of dimension through a ”quantization effect” for Toeplitz operators with i.g. non-differentiable symbols. This talk is based on joint work with L.A. Coburn (SUNY at Buffalo), R. Hagger (U. Kiel) and N. Vasilevski (CIN- VESTAV, Mexico).

References:

[1] W. Bauer, L.A. Coburn, R. Hagger, Toeplitz quantization on Fock space, J. Funct. Anal. 274 (2018), no. 12, 3531-3551.

[2] W. Bauer, R. Hagger, N. Vasilevski, Uniform continuity and quantization on bounded symmetric domains, J. Lond. Math. Soc. (2) 96 (2017), no. 2, 345-366.

[3] W. Bauer, N. Vasilevski, On algebras generated by Toeplitz operators and their rep- resentations, J. Funct. Anal. 272 (2017), 705-737.

 

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