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Applications of de Branges Spaces of Vector-Valued Functions

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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–Kreĭn 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 \(\mathcal{H}(U)\) and \(\mathcal{B}(\mathfrak{E})\), generalized Fourier transforms, direct and inverse spectral problems for regular canonical differential systems, the Kreĭn accelerant extension problem, the inverse monodromy problem, other directions. The notation is the same as in the first part.

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Authors and Affiliations

  1. South Ukrainian National Pedagogical University, Odessa, Ukraine

    Damir Z. Arov

  2. The Weizmann Institute of Science, Rehovot, Israel

    Harry Dym

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  1. Damir Z. Arov
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Correspondence to Damir Z. Arov .

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Editors and Affiliations

  1. Earl Katz Chair in Algebraic System Theory, Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Daniel Alpay

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Arov, D.Z., Dym, H. (2015). Applications of de Branges Spaces of Vector-Valued Functions. In: Alpay, D. (eds) Operator Theory. Springer, Basel. https://doi.org/10.1007/978-3-0348-0667-1_1

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