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Local scaling asymptotics for the Gutzwiller trace formula in Berezin-Toeplitz quantization. (English) Zbl 1398.32023
This paper is concerned with semiclassical aspects of the Berezin-Toeplitz quantization of a Kähler manifold $$(M, J, 2\omega )$$. The Gutzwiller trace formula deals with the asymptotics of the trace of the distributional kernel of a smoothed spectral projector relative to a spectral band of width $$O(\hbar )$$ around an energy value.
The autor studies a Gutzwiller-Toeplitz kernel from the point of view of asymptotically concentration along appropriate classical loci defined by the dynamics, with an explicit description of the exponential decay in normal directions.

##### MSC:
 32J27 Compact Kähler manifolds: generalizations, classification 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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