 00244 Matania BenArtzi, Yves Dermenjian, JeanClaude Guillot.
 Analyticity Properties and Estimates of Resolvent Kernels
near Thresholds.
(231K, Postscript)
May 26, 00

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Abstract. Resolvent estimates are derived for the family of ordinary differential
operators $\big{C^2(y)\big[\rho(y)\frac{d}{dy}\big(\frac{1}{\rho(y)}
\frac{d}{dy}\big)p^2\big]\big},\ p\in[0,\infty),\ y\in\er.$
It is assumed that $c(y)=c_{\pm}>0,\ \rho(y)=\rho_{\pm} $
for $\pm y>y_c,$ and the kernels are studied in neighborhoods of
the points $\{c^2_{pm} p^2},$ uniformly in compact intervals of $p$.
This family arises in the direct integral decomposition of the
acoustic propagator in layered media and the results imply
"low energy" estimates for the associated operator, as well as the
validity of the "limiting absorption principle".
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