Boundary Values of Regular Resolvent Families
نویسندگان
چکیده
We study properties of the boundary values (H ?i0) ?1 of the resolvent of a self-adjoint operator H for in a real open set on which H admits a locally strictly conjugate operator A (in the sense of E. Mourre, i.e. '(H) H; iA]'(H) aj'(H)j 2 for some real a > 0 if ' 2 C 1 0 (()). In particular, we determine the HH older-Zygmund class of the B(E; F)-valued maps 7 ! (H?i0) ?1 and 7 ! (H?i0)) ?1 in terms of the regularity properties of the map 7 ! e ?iAA He iAA. Here E, F are spaces from the Besov scale associated to A and are the spectral projections of A associated to the half-lines x > 0.
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