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On the point spectrum of selfadjoint extensions. (English) Zbl 0791.47005
Let H be a symmetric operator with spectral gap and infinite deficiency indices. The question is examined, to which extend the point spectrum of a selfadjoint extension H ^ of H within the set of regular points of H can be prescribed. Among others it is shown that within a spectral gap of H each kind of pure point can be generated by a selfadjoint extension of H. The question whether von Neumann’s theorem on the existence of selfadjoint extensions of C-real symmetric operators has a converse is answered (positively for deficiency (1,1), negatively for deficiency (n,n) with n>1).

47A20Dilations, extensions and compressions of linear operators
47B25Symmetric and selfadjoint operators (unbounded)
47A10Spectrum and resolvent of linear operators
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