Traces of Quantized Canonical Transformations Localized on a Finite Set of Points

For an embedding i : X ↪ M of smooth manifolds and a Fourier integral operator Φ on M defined as the quantization of a canonical transformation g: T*M \ {0} → T*M \ {0}, we consider the operator i*Φi* on the submanifold X, where i* and i* are the boundary and coboundary operators corresponding to the embedding i. We present conditions on the transformation g under which such an operator has the form of a Fourier integral operator associated with the fiber of the cotangent bundle over a point. We obtain an explicit formula for calculating the amplitude of this operator in local coordinates. © 2018, Pleiades Publishing, Ltd.

Authors
Number of issue
5
Language
English
Pages
696-707
Status
Published
Volume
54
Year
2018
Organizations
  • 1 Peoples’ Friendship University of Russia, Moscow, 117198, Russian Federation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6663/
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