Product formulas in functional calculi for sectorial operators
Charles Batty, Alexander Gomilko, Yuri Tomilov
TL;DR
This paper investigates product formulas within various functional calculi for sectorial operators, providing new theoretical results that extend and unify previous formulas across different calculus frameworks.
Contribution
It introduces a general abstract result for product formulas and derives new formulas for multiple extended functional calculi, broadening the theoretical understanding.
Findings
New product formulas for holomorphic functional calculus
Extended Stieltjes and Hille-Phillips calculus formulas
Generalization of previous work by Hirsch, Martinez, Sanz, and Schilling
Abstract
We study the product formula in the framework of (unbounded) functional calculus of sectorial operators . 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.
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