Borg–Marchenko theorem

E924204

mathematical theorem theorem in inverse spectral theory

The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.

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Label	Occurrences
Borg–Marchenko theorem canonical	1

Statements (36)

Predicate	Object
instanceOf	mathematical theorem ⓘ theorem in inverse spectral theory ⓘ
appliesTo	Sturm–Liouville operator NERFINISHED ⓘ one-dimensional Schrödinger operator ⓘ
assumes	real-valued potential ⓘ sufficient regularity of the potential ⓘ
characterizes	uniqueness of potential from spectral data ⓘ
concerns	inverse spectral problem ⓘ reconstruction of potential ⓘ spectral data of differential operators ⓘ
field	functional analysis ⓘ inverse spectral theory ⓘ mathematical physics ⓘ operator theory ⓘ spectral theory ⓘ
generalizes	Borg’s uniqueness result for Sturm–Liouville problems NERFINISHED ⓘ
hasVersion	Borg theorem NERFINISHED ⓘ Marchenko theorem NERFINISHED ⓘ
implies	uniqueness of potential for given spectral measure ⓘ
influenced	development of inverse scattering methods ⓘ theory of integrable nonlinear equations ⓘ
involves	Schrödinger operator on an interval ⓘ boundary conditions ⓘ eigenvalues ⓘ norming constants ⓘ
isPartOf	classical results in inverse spectral theory ⓘ
namedAfter	Gunnar Borg NERFINISHED ⓘ Vladimir Marchenko NERFINISHED ⓘ
relates	boundary spectral data to potential ⓘ spectral measure to potential ⓘ
states	that a potential is uniquely determined by appropriate spectral data ⓘ
topicIn	monographs on inverse spectral and scattering theory ⓘ
usedIn	integrable systems ⓘ mathematical analysis of differential equations ⓘ quantum mechanics ⓘ scattering theory ⓘ

Referenced by (1)

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Gelfand–Levitan theory → relatedTo → Borg–Marchenko theorem ⓘ