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 Mat. Zametki, 2018, Volume 104, Issue 4, Pages 588–603 (Mi mz11947)

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.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00373a Deutsche Forschungsgemeinschaft Ministry of Education and Science of the Russian Federation 5-100 This work was supported in part by the Russian Foundation for Basic Research under grant 16-01-00373a, by Deutsche Forschungsgemeinschaft (DFG), and by the “RUDN University Program 5-100.”

DOI: https://doi.org/10.4213/mzm11947

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

Bibliographic databases:

UDC: 517.95

Citation: P. A. Sipailo, “On Traces of Fourier Integral Operators on Submanifolds”, Mat. Zametki, 104:4 (2018), 588–603; Math. Notes, 104:4 (2018), 559–571

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz11947
• https://doi.org/10.4213/mzm11947
• http://mi.mathnet.ru/eng/mz/v104/i4/p588

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This publication is cited in the following articles:
1. Sipailo P.A., “Traces of Quantized Canonical Transformations on Submanifolds and Their Applications to Sobolev Problems With Nonlocal Conditions”, Russ. J. Math. Phys., 26:1 (2019), 135–138
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