Lectures related to Self-Adjoint Operators

Essential Operators: Spectrum and Resolvent Set

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

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Theory of Bounded Operators on Hilbert Space

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

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Postulates of Quantum Mechanics

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

Quantum Mechanics: Spectral Basis and Schrödinger Equation

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

Hermitian Operators and Spectral Theorem

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

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Unitary Group and Spectral Types

Covers the proof of unitary group uniqueness and spectral types.

Quantum Mechanics: Postulates and Observables

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

Functional Calculus: Self-Adjoint Operators

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

Linear Operators: Basis Transformation and Eigenvalues

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

Weak Formulation of Elliptic PDEs

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

Herglotz Representation Theorem

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

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Linear Maps and the Duality Principle in Mathematics

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

Matrix Representation of Operators and Basis Transformation

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

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.

Compositions and adjoints of unbounded operators

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.