Lectures related to Banach algebra

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

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

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Weak Solutions of Differential Equations

Explores weak solutions of differential equations and their properties.

Measure Spaces: Integration and Inequalities

Covers measure spaces, integration, Radon-Nikodym property, and inequalities like Jensen, Hölder, and Minkowski.

Cauchy-Lipschitz Theorem: Examples and Applications

Explores examples and applications of the Cauchy-Lipschitz theorem in sequences and Banach spaces.

Functional Analysis: Banach and Hilbert Spaces

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.

Linear Operators: Boundedness and Convergence

Explores linear operators, boundedness, and convergence in Banach spaces, focusing on Cauchy sequences and operator identification.

Convergence of Cauchy Sequences: Theorem Applications

Covers the convergence of Cauchy sequences and its applications in theorems.

Banach Spaces: Reflexivity and Convergence

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

Cauchy Test and Generators

Explores Cauchy test, generators, and density in functional analysis.

Normed Spaces & Reflexivity

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

Resolving Operators: Closedness and Injectivity

Discusses resolving operators' closedness and injectivity in Banach spaces.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Banach Spaces and Thermodynamic Formalism

Introduces Banach spaces for maximal entropy in billiard maps, discussing spectral bounds, norms, and measure construction.

Functional Analysis I: Operator Definitions

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

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

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

Advanced analysis II: local inversion theorem

Covers the local inversion theorem and uniqueness of solutions in a ball around a point.

Sobolev Spaces and Continuous Embeddings

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