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de Branges Spaces of Vector-Valued Functions

In: Operator Theory

Author

Listed:
  • Damir Z. Arov

    (South Ukrainian National Pedagogical University)

  • Harry Dym

    (The Weizmann Institute of Science)

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 ) $$\mathcal{B}(\mathfrak{E})$$ .

Suggested Citation

  • Damir Z. Arov & Harry Dym, 2015. "de Branges Spaces of Vector-Valued Functions," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 29, pages 721-752, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_3
    DOI: 10.1007/978-3-0348-0667-1_3
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