Hilbert Spaces: Definition and Properties

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.