10 AMREIN BOUTET DE MONVEL-BERTHIER GEORGESCU
were not required to be of compact support, but with the integrals restric-
ted to a finite interval (a,b). Then the contribution of the boundary terms
at b was estimated in the limit as b * °°. This method is explained in Sect-
5 of [5].Although the application of these results to partial differential
operators of the form (1.1) need stronger assumptions on the local behaviour
of c2, the method allows more general behaviour of c. at infinity. We shall
use it again in a subsequent paper on absence of eigenvalues for operators
that are unbounded below near infinity.
Apart from the papers already mentioned, there is a considerable
literature concerned with absence of positive eigenvalues and unique con-
tinuation properties for Schrodinger operators and more general elliptic
partial differential operators. We refer to the reference given in the re-
view by Eastham and Kalf [7] and to the recent papers by Hormander [191
and by Jerison and Kenig [20] .
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