Traces of Quantized Canonical Transformations Localized on a Finite Set of Points |
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Authors: | P. A. Sipailo |
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Affiliation: | 1.Peoples’ Friendship University of Russia,Moscow,Russia |
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Abstract: | 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. |
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