Function Spaces: Review and Compact Operators

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

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.

Distributions and Derivatives

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

Functional Analysis I: Norms and Bounded Operators

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

Continuity and Galerkin Method

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

Compact Embedding: Theorem and Sobolev Inequalities

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

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Extension of Linear Transformations

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

Functional Analysis I: Spectral Theorem

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