Concept

Weak operator topology

Related lectures (18)

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

CW Complexes

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

The Discriminant: Symmetry and Orbits

Explores the discriminant's role in equations, symmetry, and orbits in mathematical spaces.

Barycenter and Young Measures

Explains barycenter, weak convergence, uniqueness of limits, distances, and Young measures in LP spaces.

Normed Spaces & Reflexivity

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

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Sobolev Spaces and Continuous Embeddings

Covers Sobolev spaces, continuous embeddings, weak convergence, and Poincare inequalities.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

Embedding Theorems in Sobolev Spaces

Explores embedding theorems in Sobolev spaces, including continuous and compact embedding, weak convergence, and Poincaré inequality.

Weak Convergence in Hilbert Spaces

Explores weak convergence in Hilbert spaces, discussing definitions, implications, and examples.

Bolzano-Weierstrass Theorem: Sequential Compactness in Hilbert Spaces

Explores the Bolzano-Weierstrass theorem in Hilbert spaces, showcasing sequential compactness and the construction of converging subsequences.

Signals & Systems I: Fourier Transformation and Distributions

Explores the Fourier transformation, Parseval relation, weak convergence, and generalized transformations in signals and systems.

Functional Analysis I: December 16, 2021

Explores digital integration, uniform bounds, weak convergence, and norm homogeneity in functional analysis.

Functional Line: Defining Sequences and Convergence

Covers the definition of the functional line and sequences, emphasizing convergence in functional analysis.

Dual Space and Weak Convergence

Explores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.

Calculus of Variations: Ground States in Quantum Mechanics

Covers the Calculus of Variations to find ground states in quantum mechanics by minimizing energy, discussing the Euler Lagrange equation and the Fundamental Theorem of Young Measure Theory.

Embedding Theorems in Sobolev Spaces

Explores weak convergence, Poincaré inequality, and embedding theorems in Sobolev spaces.

Optimal Transport: Analysis and Proofs

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.