A Proof of the Local Borg–Marchenko Theorem

By C. Bennewitz. 2001

73 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/390445f4e7938779a569dfa33d5074d5ad3597e9

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In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Weyl-Titchmarsh M-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators (2001, methodology): “, for m = 1), by Bennewitz [13], to the current Dirac-type situation.”
A Borg–Levinson theorem for trees (2005, methodology): “Local versions of this theorem have recently been proved by Simon (1999), Gesztesy & Simon (2000) and Bennewitz (2001), the latter theorem being the result of an elegant and short proof. In the case of complex q, Brown et al. (2002) have shown, using a method modelled on the approach in Bennewitz (2”
Mathematical Methods in Quantum Mechanics (2009, unknown): “The section on inverse spectral theory presents a simple proof for the Borg–Marchenko theorem (in the local version of Simon) from Bennewitz [8].”
Uniqueness Results for Matrix-Valued Schrodinger, Jacobi, and Dirac-Type Operators (2000, methodology): “SCHRODINGER, JACOBI, AND DIRAC-TYPE OPERATORS 13¨ In the case of scalar Schr¨odinger operators, Theorem 2.13(i) is due to Simon [134]. An alternative proof was presented in [60], and more recently in [16]. Most recently, Alexander Sakhnovich kindly informed us that his integral representation of the”
On the Inverse Resonance Problem (2003, background): “A rather concise proof of this fact was given by Bennewitz in [4] who, in fact, showed that q is uniquely determined from knowing the m-function along some non-real ray.”
Inverse spectral problems and closed exponential systems (2005, methodology): “[4] Ch. Bennewitz, A proof of the local Borg-Marchenko theorem, Comm. Math.”
Equivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter (2004, unknown): “[4,11,22]), ag ain for standard boundary conditions.”