Determinants of pseudodifferential operators and complex deformations of phase space
Spectral Theory
2007-05-23 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.math/0111292,
title = {Determinants of pseudodifferential operators and complex deformations of phase space},
author = {A. Melin and J. Sjoestrand},
journal= {arXiv preprint arXiv:math/0111292},
year = {2007}
}