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This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The...
The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of high degree functions.The book develops the...
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on...
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory....
This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie...
The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method...
Complex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non-destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems encountered when using...
This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted...
This book can be divided into two parts. The ?rst part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. The raison d’ˆ etre of the book is in the second part, and so let us ?rst explain the contents of the second part. There...
Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained...
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C)...
This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is...
Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Key Features: - The Riemann hypothesis is given a natural geometric reformulation...
This book is meant for an audience of advanced undergraduates and graduate students taking courses on the statistical mechanics approach to turbulent ?ows and on stochastic simulations. It is also suitable for the self-study of professionals involved in the research and...
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their...
" About this book This book is a collection of the......
General relativity is the modern theory of the gravitational ?eld. It is a deep subject that couples ?uid dynamics to the geometry of spacetime through the Einstein equations. The subject has seen a resurgence of interest recently,...
Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of...
This book contains a systematic investigation of the convection in systems with interfaces. For the first time, it classifies all of the known types of convective instabilities in such systems, and discusses the peculiarities of multilayer systems. The book provides an...
Since the late 1980s, Toeplitz operators and matrices have remained a ?eld of extensive research and the development during the last nearly twenty years is impressive. One encounters Toeplitz matrices in plenty of applications on the one hand, and Toeplitz operators...
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