The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincare, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and...
The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curva...
Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The...
Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to expr...
Mit Hilfe der reellen Algebren der komplexen Zahlen, dualen Zahlen, anormal-komplexen Zahlen konnen Mobiusgeometrie (Geometrie der Kreise), Laguerre- bzw. Liegeometrie, pseudoeuklidische Geometrie (Minkowskigeometrie) behandelt werden. Das geschieht fiir die erst genannte Geometrie in der Geometrie der komplexen Zahlen. - Diese Zusammenhange bilden den Hintergrund des vorliegenden Buches. In Verfolg axiomatischer Begrtindungen der augegebenen Geometrien wurde del" Bereich der vorweg genannten reellen Algebren ausgedehnt: 1st Sl' ein quadratisch nicht abgeschlossener kommutativer Korper, 2...
Mit Hilfe der reellen Algebren der komplexen Zahlen, dualen Zahlen, anormal-komplexen Zahlen konnen Mobiusgeometrie (Geometrie der Kreise), Laguerre- ...
This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi- nology multistage Markovian decision processes. We discuss the applications of this theory to various concrete problems. Particular attention is paid to mathe- matical models of economic planning, taking account of stochastic factors. The authors strove to construct the exposition in such a way that a reader interested in the applications can get through the book with a minimal mathe- matical apparatus. On the other hand, a mathematician...
This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another...
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. ] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews"
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. ] the specialist, as...
This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the...
This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspec...
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrodinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the...
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those...
This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems...
This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geome...
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo...
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga...
This book considers various spaces and algebras made up of functions, measures, and other objects-situated always on one or another locally compact abelian group, and studied in the light of the Fourier transform. The emphasis is on the objects themselves, and on the structure-in-detail of the spaces and algebras. A mathematician needs to know only a little about Fourier analysis on the commutative groups, and then may go many ways within the large subject of harmonic analysis-into the beautiful theory of Lie group representations, for example. But this book represents the tendency to linger...
This book considers various spaces and algebras made up of functions, measures, and other objects-situated always on one or another locally compact ab...
