Majorization in de Branges spaces I. Representability of subspaces
نویسندگان
چکیده
In this series of papers we study subspaces of de Branges spaces of entire functions which are generated by majorization on subsets D of the closed upper half-plane. The present, first, part is addressed to the question which subspaces of a given de Branges space can be represented by means of majorization. Results depend on the set D where majorization is permitted. Significantly different situations are encountered when D is close to the real axis or accumulates to i∞. AMS Classification Numbers: 46E20, 30D15, 46E22
منابع مشابه
Majorization in de Branges spaces II. Banach spaces generated by majorants
This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banach spaces generated by admissible majorants. We study their interplay with the original de Branges space structure, and their geometry. In particular, we will show that, generically, they w...
متن کاملSubspaces of De Branges Spaces with Prescribed Growth
The growth properties of de Branges spaces and their subspaces are studied. It is shown that, for each given pair of growth functions λ(r) = O(r) and λ1 = o(λ), there exist de Branges spaces of growth λ that have a de Branges subspace of growth λ1. This phenomenon cannot occur for a class of de Branges spaces that, in a certain sense, behave regularly along the real axis. §
متن کاملWeighted Norm Inequalities for De Branges-rovnyak Spaces and Their Applications
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...
متن کاملA survey on reverse Carleson measures
This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.
متن کاملBoundary 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...
متن کامل