Linear Differential Operators
GPTKB entity
Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:actsOn |
Distributions
Function Spaces Smooth Functions |
| gptkbp:canBe |
gptkb:Elliptic
Homogeneous Parabolic Hyperbolic Non-self-adjoint Nonhomogeneous Self-adjoint |
| gptkbp:defines |
An operator L is linear if L(af+bg) = aL(f) + bL(g) for functions f, g and scalars a, b.
|
| gptkbp:example |
d/dx
d^2/dx^2 L = a_n(x) d^n/dx^n + ... + a_0(x) |
| gptkbp:field |
gptkb:Mathematics
gptkb:Differential_Equations Functional Analysis |
| gptkbp:hasProperty |
gptkb:Superposition_Principle
|
| https://www.w3.org/2000/01/rdf-schema#label |
Linear Differential Operators
|
| gptkbp:importantFor |
gptkb:Signal_Processing
gptkb:Physics gptkb:Quantum_Mechanics Engineering Control System Mathematical Modelling |
| gptkbp:mayInclude |
Constant Coefficients
Variable Coefficients |
| gptkbp:notation |
D
L |
| gptkbp:order |
Order n
|
| gptkbp:property |
Linearity
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| gptkbp:relatedTo |
gptkb:illustrator
gptkb:Kernel gptkb:Spectral_Theory Adjoint Operator Boundary Value Problems Eigenvalue Problems Green's Functions Null Space Operator Theory |
| gptkbp:studiedBy |
Mathematicians
|
| gptkbp:studiedIn |
gptkb:Ordinary_Differential_Equations
gptkb:Linear_Algebra Analysis Partial Differential Equations |
| gptkbp:usedIn |
gptkb:Ordinary_Differential_Equations
Partial Differential Equations |
| gptkbp:bfsParent |
gptkb:Cornelius_Lanczos
|
| gptkbp:bfsLayer |
6
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