Abstract
Let Σ be a symplectic manifold, H a Hilbert space. It is not possible to represent the group of symplectic automorphisms of Σ in the group of unitary operators of H in a manner nicely linked with the geometry of Σ. However if Σ is the cotangent bundle of a manifold X, unitary Fourier integral operators acting on L2(X) provide an asymptotic analogue: they move the wave front set of distributions according to some homogeneous symplectic map. (Several distinct Fourier integral operators belong to the same symplectic map.) We will describe here a similar construction for any symplectic cone with a compact basis (§3). A good model for this is given by the algebra of Toeplitz operators on a complex domain (§2). The proofs and details of our construction were published in [1].
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References
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© 1990 Kluwer Academic Publishers
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Boutet de Monvel, L. (1990). Toeplitz Operators — An Asymptotic Quantization of Symplectic Cones. In: Albeverio, S., Streit, L., Blanchard, P. (eds) Stochastic Processes and their Applications. Mathematics and Its Applications (Soviet Series), vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2117-7_6
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DOI: https://doi.org/10.1007/978-94-009-2117-7_6
Publisher Name: Springer, Dordrecht
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