Lectures related to Essential Operators: Spectrum and Resolvent Set

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.

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

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

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

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

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

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

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

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

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

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

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

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

Covers the proof of unitary group uniqueness and spectral types.

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

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

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

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

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