Hardy space H^p of the unit disk
GPTKB entity
Statements (41)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Hardy_space
function space |
| gptkbp:application |
gptkb:signal_processing
system theory prediction theory model theory for operators |
| gptkbp:basisFor |
monomials z^n
|
| gptkbp:characterizedBy |
boundary values in L^p of the unit circle
|
| gptkbp:citation |
"Hardy Spaces" by Paul Koosis
"Theory of H^p Spaces" by Peter L. Duren |
| gptkbp:consistsOf |
holomorphic functions
|
| gptkbp:contains |
gptkb:Blaschke_products
polynomials bounded analytic functions for p = inner functions outer functions |
| gptkbp:definedIn |
gptkb:unit_disk
|
| gptkbp:dualPolyhedron |
Hardy space H^q for 1/p + 1/q = 1, 1 < p <
|
| gptkbp:H1Is |
gptkb:Hilbert_space
|
| gptkbp:H2Is |
gptkb:Hilbert_space
|
| gptkbp:hasSubgroup |
holomorphic functions on unit disk
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hardy space H^p of the unit disk
|
| gptkbp:importantFor |
gptkb:Beurling's_theorem
gptkb:Fatou's_theorem complex analysis harmonic analysis Riesz factorization theorem F. and M. Riesz theorem |
| gptkbp:multiplicationOperatorIs |
bounded for p = 2
unbounded for p 0, p 1 |
| gptkbp:namedAfter |
gptkb:G._H._Hardy
|
| gptkbp:normDefinedBy |
supremum of L^p norms on circles
|
| gptkbp:parameter |
p
|
| gptkbp:range |
0 < p
|
| gptkbp:relatedTo |
gptkb:Bergman_space
Lebesgue space L^p |
| gptkbp:usedIn |
Fourier analysis
control theory operator theory |
| gptkbp:bfsParent |
gptkb:Hardy_space_H^2_of_the_unit_disk
|
| gptkbp:bfsLayer |
8
|