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Related lectures (32)

Page 2 of 4

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.