Kategoria BISAC: Mathematics >> Mathematical Analysis

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.

The first approach relies on a...

This series of volumes covers all the major aspects of numerical analysis, serving as the basic reference work on the subject. Each volume concentrates on one to three particular topics. Each article, written by an expert, is an in-depth survey, reflecting up-to-date trends in the field, and is essentially self-contained. The handbook will cover the basic methods of numerical analysis, under the following general headings: solution of equations in Rn; finite difference methods; finite element methods; techniques of scientific computing; optimization theory; and systems science. It will...

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.

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Lev...

In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity.

Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis - often with different definitions and under different names. Among the synonyms are Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called Pick functions', Nevanlinna functions' or operator monotone functions'.

This monograph - now in its second revised and extended edition - offers a self-contained and unified approach to Bernstein functions and closely related function...

This monograph is an introduction to some special aspects of topology, functional analysis, and analysis for the advanced reader. It also wants to develop a degree theory for function triples which unifies and extends most known degree theories. The book aims to be self-contained and many chapters could even serve as a basis of a course on the covered topics. Only knowledge in basic calculus and of linear algebra is assumed.

In recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such...

In this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another considered subject is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of...

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis," held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics.

The book covers the following topics:

• theory of ill-posed problems
• inverse problems for differential equations
• boundary value problems for equations of mixed type
• integral geometry
• mathematical modelling and numerical methods in natural...

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the Fejer property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative schemes. Applications to parallelization, randomization and linear programming are also considered.