Lectures related to Unitary Group and Spectral Types

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

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

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

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

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

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

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

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

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

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

Covers the representation theory of unitary minimal models and the Virasoro algebra.

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

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

Covers the concept of outer measure and properties of measurable sets.

Covers the criteria for operators to be self-adjoint and the Friedrichs extension theorem.

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

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

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

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

Explores the properties of the spectrum of an operator in L(H), including compactness and spectral radius.