Lecture

Hilbert Spaces: Definition and Properties

Related lectures (30)

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Covers the definition of a scalar product on a real vector space and provides examples.

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Offers a crash course on quantum mechanics, covering vector spaces, superposition, observables, and self-adjoint operators.

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Covers Hilbert spaces and unique solutions in function spaces, emphasizing the Lax-Milgram theorem.

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

Covers measure spaces, integration, Radon-Nikodym property, and inequalities like Jensen, Hölder, and Minkowski.

Covers normed vector spaces, including definitions, properties, examples, and sets in normed spaces.

Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.