Title: Functional calculus for Safarov pseudo-differential operators
Abstract: In 1997, Yuri Safarov introduced classes of pseudo-differential operators $\Psi_{\rho, \delta}^m\left(\Omega^\kappa, \nabla, \tau\right)$ defined via a linear connection $\nabla$ on a base manifold $M$, effectively extending the classical local Hörmander classes to a global geometric setting. This talk will begin with a brief overview of Safarov's foundational theory before presenting the construction of a holomorphic functional calculus for the case where $M$ is compact. As a primary application of this calculus, we will derive asymptotic formulas for the traces of specific operators within these classes.
Jared Wunsch
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