Published in Journal Spectral Theory, 10(2020), 747-786., 2020
Recommended citation: Gomilko, Alexander & Rzepnicki Łukasz. (2020).
Published in Mathematische Annalen, 2019
We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical Hille–Phillips functional calculus, and it is compatible with the other well-known functional calculi. It satisfies the standard properties of functional calculi, provides a unified and direct approach to a number of norm-estimates in the literature, and allows improvements of some of them.
Recommended citation: Batty, Charles & Gomilko, Alexander & Tomilov, Yuri. (2019). A Besov algebra calculus for generators of operator semigroups and related norm-estimates. Mathematische Annalen. 10.1007/s00208-019-01924-2. https://link.springer.com/article/10.1007/s00208-019-01924-2