### Synopses & Reviews

A Sequence of Problems on Semigroups consists of an arrangement of problems which are designed to develop a variety of aspects to understanding the area of one-parameter semigroups of operators. Written in the Socratic/Moore method, this is a problem book with neither the proofs nor the answers presented. To get the most out of the content requires high motivation to work out the exercises. However, the reader is given the opportunity to discover important developments of the subject and to quickly arrive at the point of independent research. Many of the problems are not found easily in other books and they vary in level of difficulty. A few open research questions are also presented. The compactness of the volume and the reputation of the author lends this concise set of problems to be a 'classic' in the making. This text is highly recommended for use as supplementary material for

#### Review

From the reviews: "The book under review is a problem book, consisting of 448 problems ... . The final chapter contains extensive notes with comments on the problems, which throw some light to the background and give hints and references to the literature. ... For an advanced graduate student, the book should serve as valuable supplement ... as well as a starting point for independent research. Intricate research problems and up-to-date treatment make the text highly recommended reading even for experts in the field." (Marjeta Kramar Fijavž, Zentralblatt MATH, Vol. 1235, 2012) "Solving the problems in the book is a very interesting enterprise, but the most beneficial thing is that these problems lead to very enlightening discussions and research problems. ... this is a very interesting book which can prove useful to graduate students and mathematicians ... . the Notes and the extended list of References are great invitations for more study and research." (Mihaela Poplicher, The Mathematical Association of America, April, 2012)

#### Review

From the reviews:

"The book under review is a problem book, consisting of 448 problems ... . The final chapter contains extensive notes with comments on the problems, which throw some light to the background and give hints and references to the literature. ... For an advanced graduate student, the book should serve as valuable supplement ... as well as a starting point for independent research. Intricate research problems and up-to-date treatment make the text highly recommended reading even for experts in the field." (Marjeta Kramar Fijavž, Zentralblatt MATH, Vol. 1235, 2012)

"Solving the problems in the book is a very interesting enterprise, but the most beneficial thing is that these problems lead to very enlightening discussions and research problems. ... this is a very interesting book which can prove useful to graduate students and mathematicians ... . the Notes and the extended list of References are great invitations for more study and research." (Mihaela Poplicher, The Mathematical Association of America, April, 2012)

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

Written in the Socratic/Moore method, this book presents a sequence of problems which develop aspects in the field of semigroups of operators. The reader can discover

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

#### Synopsis

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires

### About the Author

John W. Neuberger is a Regents Professor at the University of North Texas, Denton, TX.

### Table of Contents

-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