02-512 Jean-Marc Bouclet

Spectral distributions for long range perturbations (458K, Postscript) Dec 10, 02

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Abstract. We study distributions which generalize the concept of spectral shift function, for pseudodifferential operators on ${\mathbb R}^d$. These distributions are called spectral distributions. Relations between relative scattering determinants and spectral distributions are established; they lead to the definition of regularized scattering phases. These relations are analogous to the one valid for the usual spectral shift function. We give several asymptotics properties in the high energy and the semiclassical limits. In particular we prove Breit-Wigner formulae for the regularized scattering phases, for semiclassical Schr\"odinger operators with long range potentials.

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