On Taylor functional calculus

On the Taylor functional calculus

We give a Martinelli-Vasilescu type formula for the Taylor functional calculus and a simple proof of its basic properties.

Fractional Calculus and the Taylor-riemann Series

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...

Functional Calculus Extensions on Dual Spaces

In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absol...

Functional Calculus on BMO and related spaces

Let f be a Borel measurable function of the complex plane to itself. We consider the nonlinear operator Tf defined by Tf [g] = f ◦ g, when g belongs to a certain subspace X of the space BMO(Rn) of functions with bounded mean oscillation on the Euclidean space. In particular, we investigate the case in which X is the whole of BMO, the case in which X is the space VMO of functions with vanishing ...

Flows and stochastic Taylor series in Itô calculus