Algebras of semiclassical pseudodifferential operators associated with   Zoll-type domains in cotangent bundles
  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. 
Gerardo Hern\'andez-Due\~nas and Alejandro Uribe
math.FA math-ph math.AP math.MP