Lectures related to Functional Calculus: Operator Definition and Properties

Linear Operators: Basis Transformation and Eigenvalues

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

Theory of Bounded Operators on Hilbert Space

Explores the theory of bounded operators on Hilbert space, including adjoint properties and self-adjointness.

Functional Analysis I: Norms and Bounded Operators

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

Postulates of Quantum Mechanics

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

Matrix Representation of Operators and Basis Transformation

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

Bounded Operators: Theory and Applications

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

Essential Operators: Spectrum and Resolvent Set

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

Functional Analysis I: Operator Definitions

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

Spectral Decomposition of Bounded Self-Adjoint Operators

Explores the spectral decomposition of self-adjoint operators on Hilbert spaces.

Extension of Linear Transformations

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

Adjoint of Linear Operators on Inner Product Spaces

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Eigenvalue problem: Eigenbasis, Spectral theorem

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Linear Algebra: Vector Spaces & Operators

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Spectral Decomposition of Unbounded Operators

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Signal Representations

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

The Closed Graph Theorem

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.

Functional Calculus: Self-Adjoint Operators

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.