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.
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