Spectral Measures

Abstract

In the spectral theorems of Chapters XVIII and XIX, we defined functions of an operator f(A) with continuous functions first, and then essentially characteristic functions of an interval by a limiting process. If v is a given vector, then the association

$$ f \mapsto \left\langle {f\left( A \right)v,v} \right\rangle $$

defines a functional on C _c (R).