Schrödinger operators and de Branges spaces. (English) Zbl 1054.34019

Remling, Christian

J. Funct. Anal. 196, No. 2, 323-394 (2002).

The author gives a new view on the inverse spectral theory of one-dimensional Schrödinger operators by recognizing it as a part of the de Branges theory of Hilbert spaces of entire functions. The de Branges theorem on the connection between a regular de Branges space and canonical systems is considered as the mother of many inverse theorems.

Reviewer: Vyacheslav Pivovarchik (Odessa)

MSC:

34A55	Inverse problems involving ordinary differential equations
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
46E22	Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)

Keywords:

de Branges space; Schrödinger operator; spectral representation; inverse spectral theory

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