Matania Ben-Artzi, Yves Dermenjian, Jean-Claude Guillot.
Analyticity Properties and Estimates of Resolvent Kernels 
near Thresholds.
(231K, Postscript)

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".