Semigroups with nonquasianalytic growth
Vũ, Phóng
Studia Mathematica, Tome 104 (1993), p. 229-241 / Harvested from The Polish Digital Mathematics Library
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We study asymptotic behavior of C0-semigroups T(t), t ≥ 0, such that ∥T(t)∥ ≤ α(t), where α(t) is a nonquasianalytic weight function. In particular, we show that if σ(A) ∩ iℝ is countable and Pσ(A*) ∩ iℝ is empty, then limt→∞1/α(t)∥T(t)x∥=0, ∀x ∈ X. If, moreover, f is a function in Lα1(ℝ+) which is of spectral synthesis in a corresponding algebra Lα11(ℝ) with respect to (iσ(A)) ∩ ℝ, then limt→∞1/α(t)∥T(t)f̂(T)∥=0, where f̂(T)=ʃ0∞f(t)T(t)dt. Analogous results are obtained also for iterates of a single operator. The results are extensions of earlier results of Katznelson-Tzafriri, Lyubich-Vũ Quôc Phóng, Arendt-Batty, ..., concerning contraction semigroups. The proofs are based on the operator form of the Tauberian Theorem for Beurling algebras with nonquasianalytic weight.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:215972 
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Vũ, Phóng. Semigroups with nonquasianalytic growth. Studia Mathematica, Tome 104 (1993) pp. 229-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i3p229bwm/

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