Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.

Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.

This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one. Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras. This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.

A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces.

Picking up where the first volume left off, the book begins with a chapter on the Banach-Stone property. The authors consider the case where the isometry is from "C"0("Q," "X") to" C"0("K," "Y") so that the property involves pairs ("X," "Y") of spaces. The next chapter examines spaces "X" for which the isometries on "LP"("μ," "X") can be described as a generalization of the form given by Lamperti in the scalar case. The book then studies isometries on direct sums of Banach and Hilbert spaces, isometries on spaces of matrices with a variety of norms, and isometrieson Schatten classes. It subsequently highlights spaces on which the group of isometries is maximal or minimal. The final chapter addresses more peripheral topics, such as adjoint abelian operators and spectral isometries.

Essentially self-contained, this reference explores a fundamental aspect of Banach space theory. Suitable for both experts and newcomers to the field, it offers many references to provide solid coverage of the literature on isometries.

This volume contains a series of articles on wave phenomena and fluid dynamics, highlighting recent advances in these two areas of mathematics. The collection is based on lectures presented at the conference ""Fluids and Waves--Recent Trends in Applied Analysis"" and features a rich spectrum of mathematical techniques in analysis and applications to engineering, neuroscience, physics, and biology. The mathematical topics discussed range from partial differential equations, dynamical systems and stochastic processes, to areas of classical analysis. This volume is intended as an introduction to major topics of interest and state-of-the-art analytical research in wave motion and fluid flows. It is helpful to junior mathematicians to stay abreast of new techniques and recent trends in these areas of mathematics. The articles here also provide a unique scientific basis for recent results and new links between current research themes. In summary, this book is a guide for experts in one field to the issues of the other, and will challenge graduate students to investigate these areas of analysis in further detail.