96-506 Boutet de Monvel A., Georgescu V., Sahbani J.

Boundary Values of Regular Resolvent Families. (120K, TeX) Oct 25, 96

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Abstract. We study properties of the boundary values $(H-\gl\pm i0)^{-1}$ of the resolvent of a self-adjoint operator $H$ for $\gl$ in a real open set $\gW$ on which $H$ admits a locally strictly conjugate operator $A$ (in the sense of E.~Mourre, i.e.\ $\gf(H)^*[H,iA]\gf(H)\geq a|\gf(H)|^2$ for some real $a>0$ if $\gf\in C_0^\infty(\gW)$). In particular, we determine the H\"older-Zygmund class of the $B(\C{E};\C{F})$-valued maps $\gl \mapsto(H-\gl\pm i0)^{-1}$ and $\gl\mapsto\gP_\pm(H-\gl\pm i0))^{-1}$ in terms of the regularity \mapsto(H-\gl\pm i0)^{-1}$ and $\gl\mapsto\gP_\pm(H-\gl\pm i0))^{-1}$ in terms of the regularity properties of the map $\gt \mapsto e^{-iA\gt}He^{iA\gt}$. Here $\C{E}$, $\C{F}$ are spaces from the Besov scale associated to $A$ and $\gP_\pm$ are the spectral projections of $A$ associated to the half-lines $\pm x>0$.

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