## Differential and Integral Equations

### Resolvent kernel estimates near thresholds

#### Abstract

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.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 1 (2006), 1-14.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050529

Mathematical Reviews number (MathSciNet)
MR2192759

Zentralblatt MATH identifier
1212.35333

#### Citation

Ben-Artzi, Matania; Dermenjian, Yves; Monsef, Anton. Resolvent kernel estimates near thresholds. Differential Integral Equations 19 (2006), no. 1, 1--14. https://projecteuclid.org/euclid.die/1356050529