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The Boundary Control Approach to the Titchmarsh-Weyl m–Function. I. The Response Operator and the A–Amplitude

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Abstract

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A−amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m−function associated with the Schrödinger operator H = −∂ 2 x  + q(x) on L 2(0, ∞) with Dirichlet boundary condition at x = 0.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Alaska Fairbanks, PO Box 756660, Fairbanks, AK, 99775, USA

    Sergei Avdonin, Victor Mikhaylov & Alexei Rybkin

Authors
  1. Sergei Avdonin
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  2. Victor Mikhaylov
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  3. Alexei Rybkin
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Correspondence to Sergei Avdonin.

Additional information

Communicated by B. Simon

Dedicated with great pleasure to B.S. Pavlov on the occasion of his 70 th birthday

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Avdonin, S., Mikhaylov, V. & Rybkin, A. The Boundary Control Approach to the Titchmarsh-Weyl m–Function. I. The Response Operator and the A–Amplitude. Commun. Math. Phys. 275, 791–803 (2007). https://doi.org/10.1007/s00220-007-0315-2

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  • DOI: https://doi.org/10.1007/s00220-007-0315-2

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