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Schrödinger Operators and Canonical Systems

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Operator Theory

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Abstract

This paper discusses the inverse spectral theory of Schrödinger equations from the point of view of canonical systems and de Branges’s theory of Hilbert spaces of entire functions. The basic idea is to view Schrödinger equations as special canonical systems. For canonical systems, a complete inverse spectral theory is available: there is a one-to-one correspondence between the coefficient functions, on the one hand, and suitable spectral data, on the other hand. The task then is to identify those subclasses that correspond to Schrödinger equations.

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Authors and Affiliations

  1. Mathematics Department, University of Oklahoma, Norman, OK, USA

    Christian Remling

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  1. Christian Remling
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Correspondence to Christian Remling .

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Editors and Affiliations

  1. Ben-Gurion University of the Negev, Department of Mathematics, Beer-Sheva, Israel

    Daniel Alpay

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© 2014 Springer Basel

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Remling, C. (2014). Schrödinger Operators and Canonical Systems. In: Alpay, D. (eds) Operator Theory. Springer, Basel. https://doi.org/10.1007/978-3-0348-0692-3_10-1

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  • DOI: https://doi.org/10.1007/978-3-0348-0692-3_10-1

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  • Publisher Name: Springer, Basel

  • Online ISBN: 978-3-0348-0692-3

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