Institute of Mathematics Jena

Summer School

Spectral Theory
Schrödinger Operators

Jena, July 31 - August 3, 2018

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Kouichi Taira (University of Tokyo)
Essential self-adjointness of pseudodifferential operators

In this talk, we study the essential self-adjointness of real principal type pseudo-differential operators in a Eucliedan space. When the operator is Riemannian Laplacian, it is known that the completeness of the metric is sufficient condition for the essential self-adjointness. However, such a condition for general pseudo-differential operators is not known. We prove the essential self-adjointness under null non-trapping condition. For a proof, we employ microlocal propagation estimates in a interior region and a exterior region respectively.
This is joint work with Shu Nakamura.