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Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations (1706.09400v3)
Published 28 Jun 2017 in math.FA, math-ph, math.MP, and math.SP
Abstract: We derive a description of the family of canonical selfadjoint extensions of the operator of multiplication in a de Branges space in terms of singular rank-one perturbations using distinguished elements from the set of functions associated with a de Branges space. The scale of rigged Hilbert spaces associated with this construction is also studied from the viewpoint of de Branges's theory.