Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:signal_processing
gptkb:Control_theory Operator theory Function theory |
| gptkbp:category |
Analytic functions
Function spaces |
| gptkbp:defines |
Analytic functions on a domain that are bounded in absolute value
|
| gptkbp:domain |
Open subset of the complex plane
|
| gptkbp:field |
Complex analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Bounded Analytic Functions
|
| gptkbp:importantFor |
gptkb:Liouville's_theorem
gptkb:Montel's_theorem Maximum modulus principle |
| gptkbp:notableExample |
gptkb:Blaschke_products
Constant functions |
| gptkbp:property |
Closed under addition and multiplication
Form a Banach space with supremum norm Uniformly continuous on compact subsets |
| gptkbp:relatedTo |
gptkb:Hardy_spaces
gptkb:Liouville's_theorem Maximum modulus principle |
| gptkbp:studiedBy |
Mathematicians
|
| gptkbp:symbol |
H^1
H^2 H^4 |
| gptkbp:bfsParent |
gptkb:John_B._Garnett
gptkb:John_Garnett |
| gptkbp:bfsLayer |
6
|