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Lefschetz fixed point theorem for quantized canonical transformations. (English. Russian original) Zbl 0948.58018
Funct. Anal. Appl. 32, No. 4, 247-257 (1998); translation from Funkts. Anal. Prilozh. 32, No. 4, 35-48 (1998).
The authors prove a fixed point theorem for a trace-class Fourier integral operator associated with a quantized canonical transformation of a closed manifold cotangent space. Their analysis of the leading term of the asymptotic trace formula reveals the term dependence on the transformation fixed points. With reference to reasoning by B. V. Fedosov [in: Partial differential equations VIII. Encycl. Math. Sci. 65, 155-251 (1996; Zbl 0884.58087)], the authors show that their result generalizes the Atiyah-Bott-Lefschetz fixed point theorem.

MSC:
58J20 Index theory and related fixed-point theorems on manifolds
58J40 Pseudodifferential and Fourier integral operators on manifolds
53D22 Canonical transformations in symplectic and contact geometry
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