De Branges function

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In mathematics, a de Branges function (sometimes written as De Branges function) is a concept in functional analysis and operator theory.

A de Branges function is an entire function E from \mathbb{C} to \mathbb{C} that satisfies the inequality |E(z)| > |E(\bar z)|, for all z in the upper half of the complex plane \mathbb{C}^+ = \{z \in \mathbb{C} | {\rm Im}(z) > 0\}.

The concept is named after Louis de Branges who proved numerous results regarding the Hilbert space of these functions. These functions also figure prominently in de Branges's proof of the Bieberbach conjecture.

Given a de Branges function E, the set of all entire functions satisfying certain relationship to E is called the de Branges space of E.

[edit] References

  • Christian Remling (2003). "Inverse spectral theory for one-dimensional Schrödinger operators: the A function". Math. Z. 245.