Applications of 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 15 in Operator Theory, 2026, pp 339-362 from Springer

Abstract: Abstract This article is the second of a two part series on de Branges spaces of vector valued functions and their applications. This part focuses on applications to direct and inverse problems for canonical differential systems and Dirac–Kreı̆n systems. The exposition is again divided into a number of short sections, each of which focuses on one topic. The list of topics covered includes: spectral functions for the spaces ℋ ( U ) $$\mathcal {H}(U)$$ and ℬ ( 𝔈 ) $$\mathcal {B}(\mathfrak {E})$$ , generalized Fourier transforms, direct and inverse spectral problems for regular canonical differential systems, the Kreı̆n accelerant extension problem, the inverse monodromy problem, other directions. The notation is the same as in the first part.

Date: 2026
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DOI: 10.1007/978-3-032-16356-1_1

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