the composition of h with f. The operator S of the previous theorem is denoted h(T). More generally, a Borel functional calculus also exists for (bounded) normal operators. Resolution of the identity Let T be a self-adjoint operator. If E is a Borel subset of R, and 1E is the indicator function of E, then 1E(T) is a self-adjoint projection on H. Then mapping is a projection-valued measure called the resolution of the identity for the self adjoint operator T. The measure of R with respect to Ω is the identity operator on H. In other words, the identity operator can be expressed as the spectral integral . Sometimes the term "resolution of the identity" is also used to describe this representation of the identity operator as a spectral integral. In the case of a discrete measure (in particular, when H is finite-dimensional), can be written as in the Dirac notation, where each is a normalized eigenvector of T. The set is an orthonormal basis of H. In physics literature, using the above as heuristic, one passes to the case when the spectral measure is no longer discrete and write the resolution of identity as and speak of a "continuous basis", or "continuum of basis states", Mathematically, unless rigorous justifications are given, this expression is purely formal. References Functional calculus