Abstract.
Let –iA be the generator of a C 0-group U on a Banach space X. Via a transference principle we obtain results of the form
for certain functions f, provided that X is a UMD space. Special examples are
The first choice leads to easy proofs of the theorems of Monniaux and Dore–Venni, the second is related to a new proof of Fattorini’s theorem on cosine functions.
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Haase, M. Functional calculus for groups and applications to evolution equations. J. evol. equ. 7, 529–554 (2007). https://doi.org/10.1007/s00028-007-0313-z
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DOI: https://doi.org/10.1007/s00028-007-0313-z