Steklov operator
E910282
The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Steklov operator canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11186005 — 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: Steklov operator Context triple: [Vladimir Steklov, hasEponym, Steklov operator]
-
A.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
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B.
Fredholm operator
A Fredholm operator is a bounded linear operator between Banach (or Hilbert) spaces with finite-dimensional kernel and cokernel and a closed range, characterized by its integer-valued index.
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C.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
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D.
Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
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E.
Jacobi operator
The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
- 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: Steklov operator Target entity description: The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
-
A.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
B.
Fredholm operator
A Fredholm operator is a bounded linear operator between Banach (or Hilbert) spaces with finite-dimensional kernel and cokernel and a closed range, characterized by its integer-valued index.
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C.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
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D.
Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
-
E.
Jacobi operator
The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
boundary integral operator
ⓘ
linear operator ⓘ mathematical operator ⓘ |
| actsOn | functions on the boundary of a domain ⓘ |
| alsoCalled | Dirichlet-to-Neumann map NERFINISHED ⓘ |
| appearsIn | Calderón inverse conductivity problem NERFINISHED ⓘ |
| arisesIn |
Steklov eigenvalue problems
NERFINISHED
ⓘ
boundary value problems ⓘ elliptic partial differential equations ⓘ |
| associatedWith |
Laplace equation
NERFINISHED
ⓘ
Steklov boundary conditions NERFINISHED ⓘ harmonic functions ⓘ |
| classification | non-local boundary operator ⓘ |
| context |
Riemannian manifolds with boundary
ⓘ
bounded domains in Euclidean space ⓘ |
| dependsOn |
geometry of the domain
ⓘ
metric on the boundary ⓘ |
| domain | boundary of a domain ⓘ |
| eigenvalueProblem |
Steklov eigenfunctions
NERFINISHED
ⓘ
Steklov spectrum NERFINISHED ⓘ |
| field |
mathematical analysis
ⓘ
partial differential equations ⓘ spectral theory ⓘ |
| generalizationOf | classical Steklov boundary condition operator ⓘ |
| hasKernel | constant functions on the boundary (in many standard settings) ⓘ |
| hasProperty |
elliptic pseudodifferential operator of order 1 (on smooth boundaries)
ⓘ
positive (under suitable conditions) ⓘ self-adjoint (under suitable conditions) ⓘ |
| isDefinedFor | solutions of elliptic PDEs in a domain ⓘ |
| maps | Dirichlet boundary data to Neumann boundary data ⓘ |
| mathematicalCategory | unbounded operator on a Hilbert space (in typical formulations) ⓘ |
| namedAfter | Vladimir Andreevich Steklov NERFINISHED ⓘ |
| namedFor | Steklov eigenvalue problem NERFINISHED ⓘ |
| relatedTo |
Calderón projector
NERFINISHED
ⓘ
Neumann-to-Dirichlet map NERFINISHED ⓘ boundary integral equations ⓘ |
| requires | elliptic regularity theory for definition and analysis ⓘ |
| spectralData |
Steklov eigenvalues accumulate only at infinity
ⓘ
Steklov eigenvalues form a discrete sequence under standard assumptions ⓘ |
| typicalHilbertSpace | L^2 of the boundary measure GENERATED ⓘ |
| usedIn |
control theory for PDEs
ⓘ
inverse problems ⓘ shape optimization ⓘ spectral geometry ⓘ |
| usedToStudy |
boundary determination problems
ⓘ
relationship between boundary geometry and spectrum ⓘ |
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: Steklov operator Description of subject: The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.