A complete inner-product space. The natural setting for L² and quantum mechanics; Riesz representation and spectral theorems are key.
Hilbert space
Related concepts
- Banach space
- Inner product
- Sturm–Liouville theory
- Spectral theorem (unbounded, self-adjoint)
- Riesz representation
- Spectral theorem (compact self-adjoint)
- Von Neumann mean ergodic theorem
- Koopman operator
- Bergman kernel
- Riesz representation (1907)
- Spectral theorem (von Neumann 1929)
- Hilbert-space formulation of QM
- Franck-Condon factor |<v'|v>|^2 = S^v exp(-S)/v! (Poisson); L^2 completeness
- NV-centre diamond magnetometry: optically-detected magnetic resonance