A Besov algebra calculus for generators of operator semigroups and related norm-estimates
Published in Mathematische Annalen, 2019
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
Abstract
We construct a new bounded functional calculus for the generators of bounded semi-groups on Hilbert spaces and generators of bounded holomorphic semigroups onBanach 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 functionalcalculi. It satisfies the standard properties of functional calculi, provides a unified anddirect approach to a number of norm-estimates in the literature, and allows improve-ments of some of them.
Mathematics Subject Classification
- Primary 47A60
- Secondary 30H25 ·46E15 ·47D03