One-Parameter Semigroups for Linear Evolution Equations
Contents:
- Linear Dynamical Systems.
- Semigroups, Generators and Resolvents.
- Perturbation andApproximation of Semi groups.
- Spectral Theory for Semigroups and Generators.
- Asymptotics of Semigroups.- Semigroups Everywhere
- History ofthe Exponential Function. - Appendices
This book gives an up-to-date account of the theory of strongly
continuous one-parameter semigroups of linear operators.
lt includes a systematic discussion of the spectral theory and the long-term behavior of such semigroups.
A special feature of the text is an unusually wilde range of applications, e.g.,
to ordinary and partial differential operators, delay and Volterra equations and to control theory,
and an emphasis on Philosophical motivation and the historical background.
The book is written for students, but should also be of value for researchers interested in this field.
Nov. 1999 500pp.
0-387-98463-1 9,400.
Contents :
- Fundamental Results and Algorithms in Dedekind domains.
- Basic Relative Number Field Algorithms.
- The Fundamental Theorems of Global Class Field Theory.
- Computational Class Field Theory.- Computing Defining Equations .
- Cubic Number Fields.- Ramification, Conductors and Discriminants.
- Relative Class Groups, Units and Regulators.
- Inverting Prime Ideals. - Algorithms for p-adic fields
Sep. 1999 570 pp.
0-387-98727-4 11,420.
Finite model theory has roots in Classical model theory,
but owes its systematic development to research from complexity theory and database theory.
The book presents the main results of descriptive complexity theory, that is,
the connections between axiomatizability of classes of
finite structures and their complexity with respect to time and space bounds.
The logics that are important in this context include fixed-point logics, transitive closure logics,
and also certain infinitary languages;
their model theory is studied in full detail. Other topics include DATALOG languages,
quantifiers and oracles, 0-1 laws, optimization and approximation problems.
Aug. 1999 350 PP.
3-540-65758-4 7,580.