Determinants of pseudodifferential operators and complex deformations of phase space

A. Melin; J. Sjoestrand

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arXiv · math/0111292

Determinants of pseudodifferential operators and complex deformations of phase space

A. Melin·J. Sjoestrand

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Abstract

Consider an h-pseudodifferential operator P, whose symbol extends holomorphically to a tubular neighborhood of the real phase space and converges sufficiently fast to 1, so that the determinant of P is well-defined. We show that the modulus of this determinant is asymptotically bounded by an exponential of the integral of the logarithm of the modulus of the symbol along a certain complex deformation of the real phase space. Since there are many possible such deformations, we get a variational problem. The paper is devoted to the corresponding variational calculus.

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BibTeX RIS

A. Melin, J. Sjoestrand. 2001-11-28. Determinants of pseudodifferential operators and complex deformations of phase space. https://arxiv.org/abs/math/0111292

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