Local Dirichlet spaces as de Branges-Rovnyak spaces
نویسندگان
چکیده
منابع مشابه
Boundary behavior of functions in the de Branges–Rovnyak spaces
Abstract. This paper deals with the boundary behavior of functions in the de Branges– Rovnyak spaces. First, we give a criterion for the existence of radial limits for the derivatives of functions in the de Branges–Rovnyak spaces. This criterion generalizes a result of Ahern-Clark. Then we prove that the continuity of all functions in a de Branges– Rovnyak space on an open arc I of the boundary...
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SPACES, AND NORMS OF WEIGHTED COMPOSITION OPERATORS MICHAEL T. JURY Abstract. We prove that the norm of a weighted composition operator on the Hardy space H2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H2, and ...
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Let H(b) denote the de Branges–Rovnyak space associated with a function b in the unit ball of H∞(C+). We study the boundary behavior of the derivatives of functions in H(b) and obtain weighted norm estimates of the form ‖f ‖L2(μ) ≤ C‖f‖H(b), where f ∈ H(b) and μ is a Carleson-type measure on C+ ∪ R. We provide several applications of these inequalities. We apply them to obtain embedding theorem...
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We present an approach to de Branges’s theory of Hilbert spaces of entire functions that emphasizes the connections to the spectral theory of differential operators. The theory is used to discuss the spectral representation of one-dimensional Schrödinger operators and to solve the inverse spectral problem.
متن کاملSymmetry in de Branges almost Pontryagin spaces
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: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03896-3