Abstract
where ua(fc) = SVJjcje*** dx, and the two indirect restrictions: (i) No compound system has eigenvalues embedded in its continuous spectrum; (ii) No compound system has quasibound states (at its thresholds). The definitions of a compound system and a quasibound state will be given later. The indirect restrictions are discussed in [2] and it has been stated there without proof that they are satisfied for almost all dilation analytic short range (analytic short range potentials) potentials. The aim of this note is to present the precise statements of the results mentioned above and some ideas of their proofs. We include also some other related results. Complete proofs will be published elsewhere.
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