Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations
نویسندگان
چکیده
منابع مشابه
Rank One Perturbations, Approximations, and Selfadjoint Extensions
of a semibounded selfadjoint operator A are studied with the help of distribution theory. It is shown that such perturbations can be defined for finite values of : even if the element . does not belong to H&1(A). Approximations of the rank one perturbations are constructed in the strong operator topology. It is proven that rank one H&2 perturbations can be defined uniquely for the homogeneous o...
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Under suitable conditions on a measure, universality limits f ( ; ) that arise in the bulk, unitary case, are reproducing kernels of de Branges spaces of entire functions. In the classical case, f is the sinc kernel f (s; t) = sin (s t) (s t) ; but other kernels can arise. We study the linear operator L [h] (x) = Z 1 1 f (s; x)h (s) ds; establishing inequalities, and deducing some conditions fo...
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In many examples of de Branges spaces symmetry appears naturally. Presence of symmetry gives rise to a decomposition of the space into two parts, the ‘even’ and the ‘odd’ part, which themselves can be regarded as de Branges spaces. The converse question is to decide whether a given space is the ‘even’ part or the ‘odd’ part of some symmetric space, and, if yes, to describe the totality of all s...
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ژورنال
عنوان ژورنال: Complex Variables and Elliptic Equations
سال: 2018
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476933.2018.1536701