Directing Functionals and De Branges Space Completions in Almost Pontryagin Spaces

2017 ◽  
pp. 347-398
Author(s):  
Harald Woracek
Keyword(s):  
De Branges Space ◽  
Pontryagin Spaces

Pontryagin Spaces and Operator Colligations

1997 ◽  
pp. 1-40
Author(s):  
Daniel Alpay ◽  
Aad Dijksma ◽  
James Rovnyak ◽  
Hendrik de Snoo
Keyword(s):  
Pontryagin Spaces

Realization and Factorization in Reproducing Kernel Pontryagin Spaces

2001 ◽  
pp. 43-65
Author(s):  
D. Alpay ◽  
A. Dijksma ◽  
J. Rovnyak ◽  
H. S. V. de Snoo
Keyword(s):  
Reproducing Kernel ◽  
Pontryagin Spaces

scholarly journals Subspaces of de Branges Spaces Generated by Majorants

2009 ◽  
Vol 61 (3) ◽  
pp. 503-517 ◽  
Author(s):  
Anton Baranov ◽  
Harald Woracek
Keyword(s):  
Real Axis ◽  
Nonnegative Function ◽  
De Branges Spaces ◽  
The Real ◽  
De Branges Space

Abstract.For a given de Branges space ℋ (E ) we investigate de Branges subspaces defined in terms of majorants on the real axis. If ω is a nonnegative function on ℝ, we consider the subspaceWe show that ℛω (E ) is a de Branges subspace and describe all subspaces of this form. Moreover, we give a criterion for the existence of positive minimal majorants.

Admissible Majorants for Model Subspaces of H2, Part II: Fast Winding of the Generating Inner Function

2003 ◽  
Vol 55 (6) ◽  
pp. 1264-1301 ◽  
Author(s):  
Victor Havin ◽  
Javad Mashreghi
Keyword(s):  
Generating Functions ◽  
Unit Vector ◽  
Inner Function ◽  
Multiplier Theorem ◽  
De Branges Space ◽  
Model Subspaces ◽  
Almost Everywhere ◽  
Upper Half Plane ◽  
Logarithmic Integral ◽  
Vertical Case

AbstractThis paper is a continuation of [6]. We consider the model subspaces Kϴ = H2 ϴ ϴH2 of the Hardy space H2 generated by an inner function ϴ in the upper half plane. Our main object is the class of admissible majorants for Kϴ, denoted by Adm ϴ and consisting of all functions ω defined on ℝ such that there exists an f ≠ 0, f ∈ Kϴ satisfying |f(x)| ≤ ω(x) almost everywhere on ℝ. Firstly, using some simple Hilbert transformtechniques, we obtain a general multiplier theorem applicable to any Kϴ generated by a meromorphic inner function. In contrast with [6], we consider the generating functions ϴ such that the unit vector ϴ(x) winds up fast as x grows from –∞ to ∞. In particular, we consider ϴ = B where B is a Blaschke product with “horizontal” zeros, i.e., almost uniformly distributed in a strip parallel to and separated from ℝ. It is shown, among other things, that for any such B, any even ω decreasing on (0,∞) with a finite logarithmic integral is in Adm B (unlike the “vertical” case treated in [6]), thus generalizing (with a new proof) a classical result related to Adm exp(iσz), σ > 0. Some oscillating ω's in Adm B are also described. Our theme is related to the Beurling-Malliavin multiplier theorem devoted to Adm exp(iσz), σ > 0, and to de Branges’ space ℋ(E).

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