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arXiv · 1707.00430

Spatial asymptotics of Green's function for elliptic operators and applications: a.c. spectral type, wave operators for wave equations

Sergey A. Denisov
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Abstract

In three-dimensional case, we consider two classical operators: Schrodinger operator and an operator in the divergence form. For slowly-decaying oscillating potentials, we establish spatial asymptotics of the Green's function. The main term in this asymptotics involves vector-valued analytic function whose behavior is studied away from the spectrum. The absolute continuity of the spectrum is established as a corollary. For the operator in the divergence form, we consider the wave equation and establish existence of wave operators.

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Sergey A. Denisov. 2018-12-19. Spatial asymptotics of Green's function for elliptic operators and applications: a.c. spectral type, wave operators for wave equations. https://arxiv.org/abs/1707.00430

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