This article is cited in 3 papers

On Traces of Fourier Integral Operators on Submanifolds

P. A. Sipailo

Peoples' Friendship University of Russia, Moscow

Abstract: Given a smooth embedding of manifolds and a Fourier integral operator on the ambient manifold, the trace of this operator on the submanifold (i.e., its composition with the boundary and coboundary operators, which is an operator on the submanifold) is considered. Conditions under which such a trace is also a Fourier integral operator are determined, and its amplitude in canonical local coordinates is calculated. The results are applied to quantized canonical transformations.

Keywords: Fourier integral operators, quantized canonical transformations, traces of operators on submanifolds, relative elliptic theory, trace of a Lagrangian manifold.

UDC: 517.95

Received: 30.01.2018

DOI: 10.4213/mzm11947

 English version: Mathematical Notes, 2018, 104:4, 559–571

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