In this study, the author sets forth a unique treatment of the stability and instability of the periodic equilibria of PDE's as they relate to the notion of direct integrals. His results, and to a large extent his methods, are new. Although he aims this work at theory rather than applications, once the theoretical framework is built, applications emerge with ease. Readers with some basis in functional analysis - notably semigroups - and measure theory can strengthen their background through its introductory material on direct integrals and its proofs worked out in detail. In Stability, Instability, and Direct Integrals, applied and pure mathematicians and theoretical physicists can discover from an acknowledged innovator the most recent results of research in this active and expanding field. Readership: This book should be of interest to applied and pure mathematicians and theoretical physicists.    From The Critics   BooknewsSets forth a unique treatment of the stability and instability of the periodic equilibria of PDEs as they relate to the notion of direct integrals. Readers with some basis in functional analysis, semigroups, and measure theory can strengthen their background through introductory material on direct integrals and proofs worked out in detail. Contains chapters on areas such as reaction-diffusion systems on an infinite plate, Floquet-periodic functions, direct integrals, Navier-Stokes, spectral theory, and principles of linearized instability. Of interest to applied and pure mathematicians and theoretical physicists. Annotation c. by Book News, Inc., Portland, Or.