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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 $\stackrel{^}{H}$ 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 $\left(n,n\right)$ with $n>1$).

##### MSC:
 47A20 Dilations, extensions and compressions of linear operators 47B25 Symmetric and selfadjoint operators (unbounded) 47A10 Spectrum and resolvent of linear operators
##### References:
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