Lectures related to Continuous linear operator

Functional Analysis I: Norms and Bounded Operators

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

Bounded Operators: Theory and Applications

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

Distributions and Derivatives

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

Linear Operators: Boundedness and Spaces

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

Distributional Derivatives

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

Dual Spaces: Definitions and Properties

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

Normed Spaces

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

Functional Analysis and Distribution Theory

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

Resolving Operators: Closedness and Injectivity

Discusses resolving operators' closedness and injectivity in Banach spaces.

Extension of Linear Transformations

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

Banach Spaces: Reflexivity and Convergence

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

Functional Analysis I: Operator Definitions

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

Linear Algebra Basics

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

Continuous Functions: Definitions and Criteria

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

Linear Maps and Matrices

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Functional Analysis I

Covers sublinear functionals, linear functionals extension, and Hahn-Banach theorem.

Functional Analysis I: Spectral Theorem

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Semigroups of Linear Operators

Explores semigroups of linear operators, contraction semigroups, infinitesimal generator, and Riemann integral properties.

Operator Product Expansion

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

Calculus of Variations: Radon-Nikodym Theorem

Covers the Radon-Nikodym theorem and the uniqueness of signed Borel measures.