Concept

Auxiliary normed space

Related lectures (23)

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

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

Covers a recap of Analysis 1 and 2, emphasizing normed space R^n, subsets, and continuous functions.

Discusses well pointed spaces, neighborhoods, wedges, examples, and the universal property of the quotient.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

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

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

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

Explores advanced analysis topics, including Cauchy sequences, Banach spaces, and the Cauchy-Lipschitz theorem.

Covers normed vector spaces, topology in R^n, and the principle of drawers as a demonstration method.

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Explores the convergence proof of Stochastic Gradient Descent with strongly-convex functions and the impact of step-size on convergence properties.

Covers vector spaces, topology, and proof methods like the pigeonhole principle in R^n.

Explores norms, distances, scalar products, and norm convergence in metric spaces.

Explores norm equivalence, inverse inequality, and error analysis in finite element methods.

Explores norm equivalence in complex functions, covering homogeneity and triangular inequality.

Covers commutative diagrams, homotopy, and constructing topological spaces.

Explores equivalent norms in a vector space and their continuity properties, including proofs of norm equivalence.

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Explores the Cauchy-Schwarz inequality, norms, and inner products in a real inner product space.