## Bounds on resolvents of dilated Schrödinger operators with non trapping potentials.(English)Zbl 0607.35025

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1985, No. 1, Conf. No. 11, 7 p. (1985).
The authors obtain bounds for the resolvent of dilated Schrödinger operators. These bounds may be used to exclude resonances from the tail of the potential. The dilation used in this paper as a technical tool is the exterior complex scaling which is introduced via a separation of the laplacian in spherical co-ordinates. - A technical point concerning the exterior complex scaling (type A analyticity) has been claimed here. That this is not the case has been observed by the same authors, J. M. Combes and R. Seiler [The shape resonance, Ann. Inst. Henri Poincaré, Phys. Theor. (to appear)] and substituted by an appropriate statement.
Reviewer: H.Siedentop

### MSC:

 35J10 Schrödinger operator, Schrödinger equation 81U05 $$2$$-body potential quantum scattering theory
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