A characterization of the generators of analytic -semigroups in the class of scalar type spectral operators.

The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space $L^{2} (X, μ)$ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of $A$ and then using the Stieltjes inversion formula.

Integral transforms of vector measures on semigroups with applications to spectral operators.

W.J. Ricker (1992)

Semigroup forum

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Non-analytic local functional calculus

Ciprian Foiaş, Florian-Horia Vasilescu (1974)

Czechoslovak Mathematical Journal

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