Weyl functions and singular continuous spectra of self-adjoint extensions (Q2702374)

In his celebrated work Krein has, in particular, given first results on the spectra of self-adjoint extensions of symmetric operators with finite deficieney indices. Recently, Albeverio, Brasche, Neidhardt and Weidmann have created an inverse spectral theory for self-adjoint extensions of symmetric operators with infinite deficiency indices. In 1998, Albeverio has conjectured that for every symmetric operator \(A\) with infinite deficiency indices and a gap \(J\) and every perfect set \(F\) there exists a self-adjoint extension \(\overset\frown A\) of \(A\) such that NEWLINE\[NEWLINE\sigma_{sc}(A)\cap J= F\cap J.NEWLINE\]NEWLINE In this article the author proved that this conjecture is true at least under the additional hypothesis that \(A\) equals the orthogonal sum of infinitely many pairwise unitarily equivalent operators.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].