Functional Calculus and Borel Transform

This lecture covers the example of bounded functional calculus when PVM is defined through spectral projections of matrices, the definition of measurable functional calculus and its basic properties, and the definition of Borel transform of a measure. The slides discuss extending functional calculus to possibly unbounded operators, providing examples of PVM from matrices, and exploring the properties of normality and *-homomorphism. The lecture also delves into the concept of Herglotz function and its application in defining unbounded functions associated with vectors.