Lecture

Functional Analysis I: November 18, 2021

Related lectures (28)

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Introduces Cartesian product and induction for proofs using integers and sets.

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

Explores the composition of applications in mathematics and the importance of understanding their properties.

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Covers the concept of graph sketching with a focus on connected components.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Covers the basics of linear mapping and coordinate systems.

Explores matrix representations of linear maps and their invariance, using examples and special cases.

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Explores functional spaces, linear applications, sublinear functionals, and the Hahn-Banach theorem.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Covers weak derivatives, their properties, and applications in functional analysis.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.