De Branges space
De Branges functions
Given a de Branges function E, the de Branges space B(E) is defined as the set of all entire functions F such that
- is the open upper half of the complex plane.
- is the usual Hardy space on the open upper half plane.
A de Branges space can also be defined as all entire functions F satisfying all of the following conditions:
As Hilbert spaces
Given 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.
- Christian Remling (2003). "Inverse spectral theory for one-dimensional Schrödinger operators: the A function". Math. Z. 245.