Differential and Integral Equations

Resolvent kernel estimates near thresholds

Matania Ben-Artzi, Yves Dermenjian, and Anton Monsef

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35P05: General topics in linear spectral theory
Secondary: 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)


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

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