词条 | De Branges space |
释义 |
In mathematics, a de Branges space (sometimes written De Branges space) is a concept in functional analysis and is constructed from a de Branges function. The concept is named after Louis de Branges who proved numerous results regarding these spaces, especially as Hilbert spaces, and used those results to prove the Bieberbach conjecture. De Branges functionsA de Branges function is an entire function E from to that satisfies the inequality , for all z in the upper half of the complex plane . Definition 1Given a de Branges function E, the de Branges space B(E) is defined as the set of all entire functions F such that where:
Definition 2A de Branges space can also be defined as all entire functions F satisfying all of the following conditions: As Hilbert spacesGiven a de Branges space B(E). Define the scalar product: A de Branges space with such a scalar product can be proven to be a Hilbert space. References
2 : Operator theory|Hardy spaces |
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