Product formulas in functional calculi for sectorial operators

Abstract

We study the product formula $(fg)(A)=f(A)g(A)$ in the framework of (unbounded) functional calculus of sectorial operators $A$. We give an abstract result, and, as corollaries, we obtain new product formulas for the holomorphic functional calculus, an extended Stieltjes functional calculus and an extended Hille-Phillips functional calculus. Our results generalise previous work of Hirsch, Martinez and Sanz, and Schilling.

This is the authors accepted manuscript for a paper being published in Mathematische Zeitschrift. The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-014-1378-3

References in corpus (2)

• Generalized Stieltjes transforms: basic aspects
• Fine scales of decay of operator semigroups

Cited by in corpus (6)

• A general approach to approximation theory of operator semigroups
• On subordination of holomorphic semigroups
• On the Fundamental Principles of Unbounded Functional Calculi
• Resolvent representations for functions of sectorial operators
• A Besov algebra calculus for generators of operator semigroups and related norm-estimates
• On discrete subordination of power bounded and Ritt operators