Szegő kernel
E451540
The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concept in complex analysis
ⓘ
concept in operator theory ⓘ mathematical object ⓘ reproducing kernel ⓘ |
| appearsIn |
Hardy space theory textbooks
ⓘ
literature on several complex variables ⓘ monographs on Toeplitz operators ⓘ |
| associatedWith |
Hardy space
ⓘ
Hardy space H^2 on the unit disk ⓘ Hardy space on the unit circle ⓘ Hardy spaces on the boundary of a domain ⓘ Hilbert spaces of holomorphic functions ⓘ boundary behavior of analytic functions ⓘ orthogonal polynomials ⓘ |
| centralTo | Hardy space theory on the boundary of a domain ⓘ |
| context |
smooth bounded domains in C^n
ⓘ
strongly pseudoconvex domains ⓘ unit disk ⓘ |
| definedOn |
boundary of a domain in C^n
ⓘ
boundary of a domain in the complex plane ⓘ |
| field |
complex analysis
ⓘ
functional analysis ⓘ harmonic analysis ⓘ operator theory ⓘ |
| namedAfter | Gábor Szegő NERFINISHED ⓘ |
| property |
depends on the geometry of the boundary
ⓘ
determines an orthogonal projection onto Hardy space ⓘ gives boundary values of holomorphic functions via integral representation ⓘ is Hermitian symmetric ⓘ is positive definite ⓘ is the reproducing kernel for Hardy spaces ⓘ |
| relatedTo |
Bergman kernel
ⓘ
Cauchy integral NERFINISHED ⓘ Poisson kernel ⓘ Szegő limit theorem NERFINISHED ⓘ Szegő orthogonal polynomials ⓘ reproducing kernel Hilbert space ⓘ |
| usedIn |
CR geometry
NERFINISHED
ⓘ
Szegő projection NERFINISHED ⓘ Toeplitz operator theory NERFINISHED ⓘ approximation of analytic functions ⓘ complex geometry ⓘ prediction theory of stationary processes ⓘ projection onto Hardy spaces ⓘ scattering theory ⓘ several complex variables ⓘ spectral theory of Toeplitz operators ⓘ study of boundary values of holomorphic functions ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.