Kategoria BISAC: Mathematics >> Functional Analysis

Le but du livre est de donner aux enseignants et aux etudiants (a partir de Bac+4) en mathematiques appliquees et en mecanique des fluides un outil d'enseignement et d'apprentissage illustre par cinquante problemes accompagnes de leur correction detaillee. Ce livre presente une nouvelle methode d'analyse asymptotique pour des problemes de "couche limite." Celle-ci est appelee MASC "Methode des Approximations Successives Complementaires." La premiere moitie du livre est consacree, outre la presentation de la MASC, a ordonner les connaissances necessaires a l'analyse asymptotique et a donner...

This book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics.

This book presents a comprehensive study of boundary value problems for linear and semilinear second order elliptic equations with measure data, especially semilinear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role.

Themonograph contains a study on various function classes, a number of new results and new or easy proofs of old result (Fefferman Stein theorem on subharmonic behavior, theorem on conjugate functions on Bergman spaces), which might be interesting for specialists, a full discussion on g-function (all p > 0), and a treatment of lacunary series with values in quasi-Banach spaces.

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries.

The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the...

This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.

This unique book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space over the unit disk. Surprisingly, the key point to understanding their structure and classifying them lies in the hyperbolic geometry of the unit disk. The book develops a number of important problems whose successful solution was made possible and is based on the specific features of the Toeplitz operators from these commutative algebras.

This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.