 96506 Boutet de Monvel A., Georgescu V., Sahbani J.
 Boundary Values of Regular Resolvent Families.
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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 selfadjoint 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\"olderZygmund 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
halflines $\pm x>0$.
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