Clifford analysis
E801054
Clifford analysis is a branch of mathematical analysis that generalizes complex analysis to higher dimensions using Clifford algebras and Dirac-type operators.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf | branch of mathematical analysis ⓘ |
| developedFrom |
classical complex function theory
ⓘ
work of William Kingdon Clifford ⓘ |
| develops |
boundary value problem methods
ⓘ
function theory in Euclidean space ⓘ |
| extendsTo | higher-dimensional spaces ⓘ |
| generalizes | complex analysis ⓘ |
| generalizesConcept |
Cauchy–Riemann equations
NERFINISHED
ⓘ
holomorphic functions ⓘ |
| hasApplicationIn |
computer vision
ⓘ
control theory ⓘ elasticity theory ⓘ electromagnetism ⓘ image processing ⓘ signal processing ⓘ |
| hasKeyObject |
Cauchy kernel
ⓘ
Clifford-valued differential forms ⓘ monogenic function ⓘ |
| hasTool |
Bergman spaces
ⓘ
Cauchy integral formula NERFINISHED ⓘ Clifford wavelets NERFINISHED ⓘ Clifford-Fourier transform NERFINISHED ⓘ Hardy spaces ⓘ |
| isBasedOn |
Clifford algebras
NERFINISHED
ⓘ
Dirac operator NERFINISHED ⓘ multivector calculus ⓘ |
| isConnectedTo |
geometric calculus
ⓘ
hypercomplex analysis ⓘ quaternionic analysis ⓘ spinor fields ⓘ |
| isPartOf |
geometric analysis
ⓘ
harmonic analysis ⓘ |
| isRelatedTo |
Dirac equation
NERFINISHED
ⓘ
mathematical physics ⓘ partial differential equations ⓘ potential theory ⓘ quantum mechanics ⓘ representation theory ⓘ spin geometry ⓘ |
| studies |
Clifford-valued functions
ⓘ
Dirac-type operators ⓘ monogenic functions ⓘ |
| uses | Clifford algebra NERFINISHED ⓘ |
| usesOperator |
Cauchy transform
NERFINISHED
ⓘ
Dirac operator NERFINISHED ⓘ Laplacian NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.