Lectures related to Continuous linear operator

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

Functional Analysis and Distribution Theory

Explores different notions of function equality, linear functionals, operations on distributions, and the advantages of working with Schwartz' space.

Continuous Functions: Definitions and Criteria

Covers the definition and criteria for continuous functions and explores the intermediate value theorem.

Operator Product Expansion

Explores Operator Product Expansion (OPE) and its role in Conformal Bootstrap.

The Closed Graph Theorem

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Properties of Complete Spaces

Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Quantum Field Theory: Exo Session 4

Covers exercises on Schur's lemma and the Jacobi identity in Quantum Field Theory.

Functional Analysis I: Norms and Bounded Operators Log in to Mediaspace to watch this video

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Distributions and Derivatives Log in to Mediaspace to watch this video

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

Linear Operators: Boundedness and Spaces Log in to Mediaspace to watch this video

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Distributional Derivatives Log in to Mediaspace to watch this video

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Dual Spaces: Definitions and Properties Log in to Mediaspace to watch this video

Covers the definitions and properties of dual spaces and linear operators.

Normed Spaces Log in to Mediaspace to watch this video

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

Resolving Operators: Closedness and Injectivity Log in to Mediaspace to watch this video

Discusses resolving operators' closedness and injectivity in Banach spaces.

Extension of Linear Transformations Log in to Mediaspace to watch this video

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Banach Spaces: Reflexivity and Convergence Log in to Mediaspace to watch this video

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

Functional Analysis I: Operator Definitions Log in to Mediaspace to watch this video

Introduces linear and bounded operators, compact operators, and the Banach space.

Linear Algebra Basics Log in to Mediaspace to watch this video

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.