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

作者：Hernandez Duenas Gerardo; Uribe Alejandro^*

来源：Journal of Functional Analysis, 2015, 268(7): 1755-1807.

DOI：10.1016/j.jfa.2014.12.004

• Pseudodifferential operators
• Fourier integral operators
• Quantization of symplectic manifolds

We 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 Szego limit theorem, and study associated propagators.

• 出版日期2015-4-1