فضاء هلبرت

Hilbert spaces can be used to study the harmonics of vibrating strings.

فضاء هيلبرت هوفضاء معياري معهد عليه دالة الضرب الداخلي بشرط حتىقد يكون المعيار المعهد عليه هوبدلالة دالة الضرب الداخلي هذه, بالإضافة إلى وجوب كونه فضاء معياري تام أوما يدعى ب فضاء باناخ. وهذا يعني حتى أي فضاء هيلبرت هوفضاء باناخ ولكن العكس غير سليم.

مقدمة وتاريخ

David Hilbert, the mathematician whose groundbreaking work on the study of integral equations and quadratic forms led to the introduction of the Hilbert space.

التطبيقات

The orbitals of an electron in a hydrogen atom are eigenfunctions of the energy. The energy is given by the (time-independent) Schrödinger operator acting on a dense subspace of the Hilbert space of square-integrable functions on R³, and its spectrum determines the possible energy levels.

Parallelogram identity and polarization

Geometrically, the parallelogram identity asserts that AC² + BD² = 2(AB² + AD²). In words, the sum of the squares of the diagonals is twice the sum of the squares of any two adjacent sides.

طالع ايضاً

هناك كتاب ، Functional Analysis/Hilbert spaces، في فهم الخط.

Harmonic analysis
Hermitian operators
Hilbert C*-module
Hilbert manifold
Mathematical analysis
Operator algebra
Rigged Hilbert space
Reproducing kernel Hilbert space
Topologies on the set of operators on a Hilbert space

الهامش

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