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On extensions of Hermitian functions with a finite number of negative squares. (English) Zbl 0996.47012

Summary: We study extensions of a Hermitian function \(f\) with a finite number of negative squares given on a finite interval to the whole real axis. We associate to \(f\) an (in general degenerated) inner product space and a symmetric relation and use the theory of selfadjoint extensions in order to describe all extensions of \(f\).

MSC:

47A20 Dilations, extensions, compressions of linear operators
47B50 Linear operators on spaces with an indefinite metric
42A82 Positive definite functions in one variable harmonic analysis
47A57 Linear operator methods in interpolation, moment and extension problems
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