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Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations
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math.FAmath-phmath.MPmath.SP
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brangesassociatedextensionsmultiplicationoperatorperturbationsrank-oneselfadjoint
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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.
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