Gelfand–Levitan theory
E270386
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Gelfand–Levitan integral equation | 1 |
| Gelfand–Levitan theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2475514 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Gelfand–Levitan theory Context triple: [Israel Gelfand, knownFor, Gelfand–Levitan theory]
-
A.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
B.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
C.
Wiener–Khinchin theorem
The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
-
D.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
E.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Gelfand–Levitan theory Target entity description: Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
-
A.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
B.
Carathéodory–Fejér interpolation
Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
-
C.
Wiener–Khinchin theorem
The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
-
D.
Selberg integral
The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
-
E.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
inverse spectral theory
ⓘ
mathematical theory ⓘ |
| aimsTo |
reconstruct differential operators
ⓘ
reconstruct potentials ⓘ |
| appliesTo |
Schrödinger operators
ⓘ
Sturm–Liouville problem ⓘ
surface form:
Sturm–Liouville operators
|
| assumes | self-adjointness of operators ⓘ |
| basedOn |
eigenvalues
ⓘ
norming constants ⓘ spectral measure ⓘ |
| characteristicFeature |
formulation as a Volterra-type integral equation
ⓘ
reconstruction from spectral data ⓘ |
| concerns | one-dimensional second-order differential operators ⓘ |
| coreConcept |
Gelfand–Levitan theory
self-linksurface differs
ⓘ
surface form:
Gelfand–Levitan integral equation
|
| developedIn | 20th century ⓘ |
| field |
functional analysis
ⓘ
inverse problems ⓘ mathematical physics ⓘ spectral theory ⓘ |
| hasApplicationIn |
integrable systems
ⓘ
quantum mechanics ⓘ vibrating strings ⓘ |
| influenced |
development of integrable PDE theory
ⓘ
modern inverse scattering methods ⓘ |
| involves |
Green functions
ⓘ
resolvent operators ⓘ |
| namedAfter |
Boris Levitan
ⓘ
Israel Gelfand ⓘ |
| provides |
existence results for inverse spectral problems
ⓘ
uniqueness results for inverse spectral problems ⓘ |
| relatedTo |
Borg–Marchenko theorem
ⓘ
Marchenko theory ⓘ direct spectral problem ⓘ scattering theory ⓘ |
| solves | inverse Sturm–Liouville problem ⓘ |
| typicalInput |
continuous spectrum
ⓘ
discrete spectrum ⓘ |
| typicalOutput |
coefficient of differential operator
ⓘ
potential function ⓘ |
| uses |
integral equations
ⓘ
kernel functions ⓘ spectral data ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Gelfand–Levitan theory Description of subject: Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gelfand–Levitan integral equation