The Asymptotic Behaviour of Semigroups of Linear Operators
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
1996, 1996
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| Edition: | 1st ed. 1996 |
| Series: | Operator Theory: Advances and Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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