de Branges Spaces of Vector-Valued Functions

Damir Z. Arov () and Harry Dym ()
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Damir Z. Arov: South Ukrainian National Pedagogical University
Harry Dym: The Weizmann Institute of Science

Chapter 29 in Operator Theory, 2015, pp 721-752 from Springer

Abstract: Abstract This article is the first of a two-part series on de Branges spaces of vector valued functions and some of their applications to direct and inverse problems for canonical differential systems and Dirac–Kreĭn systems. This first part is intended as an introduction to the spaces; the second, which is written as a continuation of the first, will focus on applications. The exposition is divided into a number of short sections, each of which deals with one topic. The list of topics covered in this part includes: reproducing kernel Hilbert spaces, J-inner matrix valued functions and some of their important subclasses, the Potapov–Ginzburg transform, linear fractional transformations, the de Branges spaces ℋ ( U ) $$\mathcal{H}(U)$$ , the de Branges space ℬ ( 𝔈 ) $$\mathcal{B}(\mathfrak{E})$$ .

Keywords: Potapov Ginzburg Transform; Reproducing Kernel Hilbert Space (RKHS); Linear Fractional Transformation; Reproducing Kernel (RK); Canonical Differential Systems (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_3

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DOI: 10.1007/978-3-0348-0667-1_3

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