Functional Analysis I: Foundations and Applications

Related lectures (29)

Page 3 of 3

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

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

Covers the construction and properties of CW complexes, including weak topology and characteristic maps.

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

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Explores open sets, compactness, and connectivity in topology, covering topological spaces and compact sets.

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.