Lectures related to Functional Calculus and Borel Transform

Domain and Graph of Unbounded Operators

Covers the fundamental concepts of unbounded operators in quantum physics, focusing on defining a functional calculus and spectral decomposition.

Spectral Decomposition of Bounded Self-Adjoint Operators

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

Linear Operators: Basis Transformation and Eigenvalues

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

Quantum Mechanics: Postulates and Observables

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

Matrix Representation of Operators and Basis Transformation

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

Linear Operators: Quantum Mechanics and Linear Algebra

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Functional Calculus: Operator Definition and Properties

Explores the definition and properties of the functional calculus for self-adjoint and bounded 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.

Hermitian Operators and Spectral Theorem

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian 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.

Postulates of Quantum Mechanics

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

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

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.

Eigenvalue problem: Eigenbasis, Spectral theorem

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

Functional Calculus: Simple Functions Log in to Mediaspace to watch this video

Covers the extension of functional calculus to simple functions and the concept of *-homomorphism.

Quantum Mechanics: Spectral Basis and Schrödinger Equation Log in to Mediaspace to watch this video

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.

Functional Calculus: Self-Adjoint Operators Log in to Mediaspace to watch this video

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

Herglotz Representation Theorem Log in to Mediaspace to watch this video

Covers the Herglotz representation theorem and the construction of projection-valued measure.

Linear Algebra: Unitary Operators Log in to Mediaspace to watch this video

Delves into unitary operators, self-adjoint properties, and spectral theorems in linear algebra.

Unitary Group and Spectral Types Log in to Mediaspace to watch this video

Covers the proof of unitary group uniqueness and spectral types.