On the Trace Approach to the Inverse Scattering Problem in Dimension One

DOI10.1137/S0036141000365620zbMath0988.34068OpenAlexW2094996289MaRDI QIDQ2706232

Alexei Rybkin

Publication date: 19 March 2001

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036141000365620

zbMATH Keywords

inverse scatteringtrace formulasKrein's spectral shift functionWeyl's m-function

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Weyl theory and its generalizations for ordinary differential equations (34B20) Inverse problems involving ordinary differential equations (34A55) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (5)

Asymptotics of the Weyl function for Schrödinger operators with measure-valued potentials ⋮ Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators ⋮ Spectral properties of a class of reflectionless Schrödinger operators ⋮ On a complete analysis of high-energy scattering matrix asymptotics for one dimensional Schrödinger operators with integrable potentials ⋮ Necessary and sufficient conditions for absolute summability of the trace formulas for certain one dimensional Schrödinger operators

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