-Preface.-1. Introduction.-2. The idea of a semigroup.-3. Translation semigroups.-4. Linear continuous semigroups.-5.Strongly continuous linear semigroups.-6. An Application to the Heat Equation.-7. Some Problems in Analysis.-8.Semigroups of steepest descent.-9. Numerics of semigroups of steepest descent.-10. Nonlinear semigroups studied by linear methods.-11. Measures and linear extension of nonlinear semigroups.-12. Local semigroups and Lie generators.-13. Quasi-analyticity of semigroups.-14. Continuous Newton's method and semigroups-15. Generalized semigroups without forward uniqueness.-16. Semigroups of nonlinear contractions and monotone operators.-17. Notes.-18. References.
Über den Autor
John W. Neuberger is a Regents Professor at the University of North Texas, Denton, TX. He received his PhD at 22 from the University of Texas, completing both undergraduate and graduate work in 6 years. Neuberger has been a strong advocate of the Moore (Socratic) method of teaching during his long career in mathematics and is well respected in the fields of PDEs, numerical analysis, functional analysis, real variables, superconductivity, and algebraic geometry. His motto is: "when a man learns to teach himself, there is nothing more we can do for him."
Written in the Socratic/Moore method style and provision of references, enables the motivated student to arrive at the point of independent research
Student who works through the problems will have a range of introduction to aspects of one-parameter semigroups of transformations
Problems include wide applicability to probability and the Heat equation