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arXiv · 1105.5471

Algebras of semiclassical pseudodifferential operators associated with Zoll-type domains in cotangent bundles

Gerardo Hernández-Dueñas·Alejandro Uribe
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Abstract

We are consider domains in cotangent bundles with the property that the null foliation of their boundary is fibrating and the leaves satisfy a Bohr-Sommerfeld condition (for example, the unit disk bundle of a Zoll metric). Given such a domain, we construct an algebra of associated semiclassical pseudodifferential operators with singular symbols. The Schwartz kernels of the operators have frequency set contained in the union of the diagonal and the flow-out of the null foliation of the boundary of the domain. We develop a symbolic calculus, prove the existence of projectors (under a mild additional assumption) whose range can be thought of as quantizing the domain, give a symbolic proof of a Szeg\"o limit theorem, and study associated propagators.

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Gerardo Hernández-Dueñas, Alejandro Uribe. 2011-05-27. Algebras of semiclassical pseudodifferential operators associated with Zoll-type domains in cotangent bundles. https://arxiv.org/abs/1105.5471

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