One-parameter groups of regular quasimultipliers

Groups of unbounded operators are approached in the setting of the Esterle quasimultiplier theory. We introduce groups of regular quasimultipliers of growth ω, or ω-groups for short, where ω is a continuous weight on the real line. We study the relationship of ω-groups with families of operators and...

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Bibliographic Details
Published in:Journal of functional analysis 2006-08, Vol.237 (1), p.1-53
Main Authors: Galé, José E., Miana, Pedro J.
Format: Article
Language:English
Subjects:
Banach algebras
Fractional calculus
Functional calculus
Groups of unbounded operators
Holomorphic semigroups
Multipliers
Quasimultipliers
Regularized, distribution and integrated groups
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Summary:Groups of unbounded operators are approached in the setting of the Esterle quasimultiplier theory. We introduce groups of regular quasimultipliers of growth ω, or ω-groups for short, where ω is a continuous weight on the real line. We study the relationship of ω-groups with families of operators and homomorphisms such as regularized, distribution and integrated groups, holomorphic semigroups, and functional calculi. Some convolution Banach algebras of functions with derivatives to fractional order are needed, which we construct using the Weyl fractional calculus.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2006.03.021