00-244 Matania Ben-Artzi, Yves Dermenjian, Jean-Claude 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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