## Some expamples of smooth operators and the associated smoothing effect.(English)Zbl 0833.47005

The main purpose of this paper is to give some examples of $$(-\Delta)$$- supersmooth operators and to show a new result on scattering theory for vaguely decaying potentials $$V\in L^p (\mathbb{R}^m)$$, $$m/2\leq p< (m+ 1)/2$$.

### MSC:

 47A40 Scattering theory of linear operators 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47A10 Spectrum, resolvent
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