Kategoria BISAC: Mathematics >> Mathematical Analysis

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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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.

This is a proceedings of the international conference "Painleve Equations and Related Topics" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the SteklovInstitute of Mathematicsof theRussian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011.

The survey articles discuss the following topics:

• General ordinary differential equations
• Painleve equations and their generalizations
• Painleve property
• Discrete Painleve equations
• Properties of solutions of all mentioned above...

This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible...