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AuthorNeerven, Jan van. author
TitleThe Asymptotic Behaviour of Semigroups of Linear Operators [electronic resource] / by Jan van Neerven
ImprintBasel : Birkhรคuser Basel, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-0348-9206-3
Descript XII, 241 p. online resource

CONTENT

1. Spectral bound and growth bound -- 1.1. C0โ{128}{148}semigroups and the abstract Cauchy problem -- 1.2. The spectral bound and growth bound of a semigroup -- 1.3. The Laplace transform and its complex inversion -- 1.4. Positive semigroups -- Notes -- 2. Spectral mapping theorems -- 2.1. The spectral mapping theorem for the point spectrum -- 2.2. The spectral mapping theorems of Greiner and Gearhart -- 2.3. Eventually uniformly continuous semigroups -- 2.4. Groups of non-quasianalytic growth -- 2.5. Latushkin - Montgomery-Smith theory -- Notes -- 3. Uniform exponential stability -- 3.1. The theorem of Datko and Pazy -- 3.2. The theorem of Rolewicz -- 3.3. Characterization by convolutions -- 3.4. Characterization by almost periodic functions -- 3.5. Positive semigroups on Lp-spaces -- 3.6. The essential spectrum -- Notes Ill -- 4. Boundedness of the resolvent -- 4.1. The convexity theorem of Weis and Wrobel -- 4.2. Stability and boundedness of the resolvent -- 4.3. Individual stability in B-convex Banach spaces -- 4.4. Individual stability in spaces with the analytic RNP -- 4.5. Individual stability in arbitrary Banach spaces -- 4.6. Scalarly integrable semigroups -- Notes -- 5. Countability of the unitary spectrum -- 5.1. The stability theorem of Arendt, Batty, Lyubich, and V? -- 5.2. The Katznelson-Tzafriri theorem -- 5.3. The unbounded case -- 5.4. Sets of spectral synthesis -- 5.5. A quantitative stability theorem -- 5.6. A Tauberian theorem for the Laplace transform -- 5.7. The splitting theorem of Glicksberg and DeLeeuw -- Notes -- Append -- Al. Fractional powers -- A2. Interpolation theory -- A3. Banach lattices -- A4. Banach function spaces -- References -- Symbols


Mathematics Functional analysis Operator theory Mathematics Operator Theory Functional Analysis



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