Functional Calculus: Self-Adjoint Operators

This lecture covers the concept of self-adjoint operators, including the Weyl criterion and the motivation for functional calculus. The instructor explains the relationship between symmetric operators and real spectrum, using examples like the Schrödinger operator. The lecture progresses to discuss the inverse of the spectrum and the resolvent of operators. The importance of self-adjoint operators over symmetric ones is highlighted, leading to the introduction of the functional calculus. The presentation follows the chronological order of the slides, starting with the definition of self-adjoint operators and concluding with the need for a theory for general versions of functional calculus.