Bøger i Mathematical Surveys and Monographs serien

Presents a geometric theory for incompressible flow and its applications to fluid dynamics. This monograph intends to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. It is suitable for researchers interested in nonlinear PDEs and fluid dynamics.

Presents an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. This book contains several topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.

Deals with the study of algebras of functions on quantum groups. This book includes the theory of Poisson Lie groups (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions, and the theory of quantum Weyl groups.

Presents a study of polynomial identities by combining methods of ring theory, combinatorics, and representation theory of groups with analysis. This book includes such topics as polynomial rings in one or several variables, the Grassmann algebra, and finite-dimensional algebras. It is suitable for students of polynomial identity algebras.

Over the years, the theory of Bergman spaces has undergone a remarkable metamorphosis. The subject of Bergman spaces is a masterful blend of complex function theory with functional analysis and operator theory. This book is suitable for those who have studied basic complex function theory, measure theory, and functional analysis.

Around 1980, G Mason announced the classification of a certain subclass of a class of finite simple groups known as 'quasithin groups'. The classification of the finite simple groups depends upon a proof that there are no unexpected groups in this subclass. This book offers a proof of a theorem classifying a larger class of groups.

Around 1980, G Mason announced the classification of a certain subclass of a class of finite simple groups known as 'quasithin groups'. The classification of the finite simple groups depends upon a proof that there are no unexpected groups in this subclass. This book offers a proof of a theorem classifying a larger class of groups.

Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy theoretic ideas are becoming important, such as algebraic $K$-theory and algebraic geometry. Suitable for graduate level, this title intends to obtain a deeper understanding of Quillen's model categories.

Presents some gratuitous generalities on scientific method as it relates to diffusion theory. This book defines Brownian motion by the characterization of P Levy, and then constructed in three basic ways and these are proved to be equivalent in the appropriate sense.

Aims to treat a theory of elliptic boundary value problems in domains without singularities and in domains with conical or cuspidal points. This work focuses on fundamental results of the theory: estimates for solutions in different function spaces, regularity assertions and asymptotic formulas for the solutions near singular points.

Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.

This is the first book to be devoted entirely to the potential theory of the heat equation, and thus deals with time dependent potential theory. Its purpose is to give a logical, mathematically precise introduction to a subject where previously many proofs were not written in detail, due to their similarity with those of the potential theory of Laplace's equation.

Offers a self-contained presentation of classical methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. This book is suitable for students and mature scientists interested in nonlinear wave phenomena.

Discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the Bott - Borel - Weil theorem, which is used as an important tool. This book provides a description of the geometry and its basic invariants.

Explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations.

Focuses on the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J Mather on hyperbolic dynamical systems and J Howland on nonautonomous Cauchy problems. This book includes a collection of examples from different areas of analysis, PDEs, and dynamical systems.

Studies nonlocal bifurcations that occur on the boundary of the domain of Morse-Smale systems in the space of all dynamical systems. This work presents the foundations of normal forms and hyperbolic theories from the very first stages. The proofs are preceded by heuristic descriptions of the ideas.

Riesz space (or a vector lattice) is an ordered vector space that is simultaneously a lattice. A topological Riesz space (also called a locally solid Riesz space) is a Riesz space equipped with a linear topology that has a base consisting of solid sets. This book presents a study (with complete proofs) of topological Riesz spaces.

Provides a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Much of the content has never before appeared in book form.

Much has been written on the theory of discontinuous groups and automorphic functions since 1880, when the subject received its first formulation. This book intends to bring together in one place both the classical and modern aspects of the theory, and to present them clearly and in a modern language and notation.

Intends to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second-order elliptic quasilinear equations in divergence form. This book concludes with a chapter dealing with existence theory.