Open Access
2006 Resolvent kernel estimates near thresholds
Matania Ben-Artzi, Yves Dermenjian, Anton Monsef
Differential Integral Equations 19(1): 1-14 (2006). DOI: 10.57262/die/1356050529


The paper deals with the spectral structure of the operator $ H=-\nabla\cdot b \nabla $ in $\mathbb R^n$ where $b$ is a stratified matrix-valued function. Using a partial Fourier transform, it is represented as a direct integral of a family of ordinary differential operators $H_p,\, p\in \mathbb{R}^n.$ Every operator $H_p$ has two thresholds and the kernels are studied in their (spectral) neighborhoods, uniformly in compact sets of $p$. As in [3], such estimates lead to a limiting absorption principle for $H$. Furthermore, estimates of the resolvent of $H$ near the bottom of its spectrum ("low energy" estimates) are obtained.


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Matania Ben-Artzi. Yves Dermenjian. Anton Monsef. "Resolvent kernel estimates near thresholds." Differential Integral Equations 19 (1) 1 - 14, 2006.


Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35333
MathSciNet: MR2192759
Digital Object Identifier: 10.57262/die/1356050529

Primary: 35P05
Secondary: 47F05

Rights: Copyright © 2006 Khayyam Publishing, Inc.

Vol.19 • No. 1 • 2006
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