A Besov class functional calculus for bounded holomorphic semigroups |
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Authors: | Pascale Vitse |
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Affiliation: | Abteilung Angewandte Analysis, Fakultät für Mathematik und Wirtschaftswissenschaften, Universität Ulm, Helmholtzstr. 18 (Raum E61), DE-89069 Ulm, Germany |
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Abstract: | It is well-known that -sectorial operators generally do not admit a bounded H∞ calculus over the right half-plane. In contrast to this, we prove that the H∞ calculus is bounded over any class of functions whose Fourier spectrum is contained in some interval [ε,σ] with 0<ε<σ<∞. The constant bounding this calculus grows as as and this growth is sharp over all Banach space operators of the class under consideration. It follows from these estimates that -sectorial operators admit a bounded calculus over the Besov algebra of the right half-plane. We also discuss the link between -sectorial operators and bounded Tadmor-Ritt operators. |
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Keywords: | Functional calculus Bounded holomorphic semigroups Sectorial operators Tadmor-Ritt operators Besov spaces in the half plane |
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