The analytic model represents a subnormal operator as the multiplication by the independent variable of a space of vector-valued functions that are analytic on the

resolvent set of its normal extension, says Xia.

1] := ([lambda]I-A)x[parallel], x [member of] D(A) (for some [lambda] fixed in the

resolvent set [rho](A) of A), and [X.

alpha]] : Re([lambda]) > [omega]} [subset] [rho](A)) ([rho](A) being the

resolvent set of A) and

We denote by [rho](A) the

resolvent set of A and by [sigma](A) the spectrum of A.

where [rho](T) = C\[sigma](T) is the resolvent set of T.

iso](T) denotes the set of all isolated points of [sigma]'(T), and [rho](T) = C\[sigma]'(T) is the resolvent set of T [member of] A' with respect to A'.

The last theorem that we state in this section shows that the point spectrum, continuous spectrum, and

resolvent set of a self-adjoint operator A and each of its associated left-definite operators [A.

11), the scheme Solve with the scaling D would indeed work for each fixed 7 in the

resolvent set with optimal complexity.