Our purpose and main concern in writing this book is to illuminate classical concepts from the noncommutative viewpoint, to make the language and techniques of noncommutative geometry accessible and familiar to practi- tioners of classical mathematics, and to benefit physicists interested in the uses of noncommutative spaces. Same may say that ours is a very "com- mutative" way to deal with noncommutative matters; this charge we readily admit. Noncommutative geometry amounts to a program of unification of math- ematics under the aegis of the quantum apparatus, i.e., the theory of ope- rators...
Our purpose and main concern in writing this book is to illuminate classical concepts from the noncommutative viewpoint, to make the language and tech...
This book offers an elementary, self-contained approach to the mathematical theory of viscous, incompressible fluid in a domain of the Euclidian space, described by the equations of Navier-Stokes. It is the first to provide a systematic treatment of the subject. It is designed for students familiar with basic tools in Hilbert and Banach spaces, but fundamental properties of, for example, Sobolev spaces, are collected in the first two chapters.
This book offers an elementary, self-contained approach to the mathematical theory of viscous, incompressible fluid in a domain of the Euclidian sp...
The discoveries of the past decade have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic map- pings is very different from that of volume preserving mappings which raised new questions, many of them still unanswered. On the other hand, due to the analysis of an old variational principle in classical mechanics, global periodic phenomena in Hamiltonian systems have been established. As it turns out, these seemingly differ- ent phenomena are...
The discoveries of the past decade have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: sympl...
In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material and organized the content slightly differently.
In particular, we included evolutionary equations and differential equations on...
In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method consider...
This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.
This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. Al...
