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＜E-Book＞
The Asymptotic Behaviour of Semigroups of Linear Operators / by Jan van Neerven
(Operator Theory: Advances and Applications. ISSN:22964878 ; 88)

Edition	1st ed. 1996.
Publisher	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
Year	1996
Language	English
Size	XII, 241 p : online resource
Authors	*Neerven, Jan van author SpringerLink (Online service)
Subjects	LCSH:Operator theory LCSH:Functional analysis FREE:Operator Theory FREE:Functional Analysis
Notes	1. Spectral bound and growth bound -- 1.1. C0—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 HTTP:URL=https://doi.org/10.1007/978-3-0348-9206-3

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