Functional Analysis I: Operator Definitions

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Page 3 of 4

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Function Spaces: Review and Compact Operators

Covers the review of function spaces and explores the concept of compact operators.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Convergent Sequences: Definitions and Illustrations

Explains convergent sequences, bounded sequences, subsequences, and compact sets with illustrations and proofs.

Linear Operators and Bounded Domains

Covers linear operators and bounded domains, focusing on the existence of such operators in domains with bounded boundaries.

Functional Analysis and Distribution Theory

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

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Interior Points and Compact Sets

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.