Calculus and mathematical analysis Books

1.Introduction to the problem.- 2.Sobolev spaces.- 3.Exitence, Uniqueness of basic problems.- 4.Regularity of solution.- 5.Applications of Rellich's inequalities and generalization to boundary value problems.- 6.Sobolev spaces with weights and...

Generalized Convex Functions.- Generalized Type I and Related Functions.- Optimality Conditions.- Duality Theory.- Second and Higher Order Duality.- Symmetric Duality.- Vector Variational-like Inequality Problems.

Preface.- Introduction.- Unwinding of proofs (`Proof Mining').- Intuitionistic and classical arithmetic in all finite types.- Representation of Polish metric spaces.- Modified realizability.- Majorizability and the fan rule.- Semi-intuitionistic systems...

Preliminaries.- The Jordan normal form of the Coxeter transformation.- Eigenvalues, splitting formulas and diagrams Tp,q,r.- R. Steinberg's theorem, B. Kostant's construction.- The affine Coxeter transformation.

Integrable Hamiltonian Hierarchies: Spectral Methods.- The Lax Representation and the AKNS Approach.- The Direct Scattering Problem for theZakharov-Shabat System.- The Inverse Scattering Problem for the Zakharov-Shabat System.- The Generalized Fourier...

The Direct Methods in the Calculus of Variations.- Minimax Methods.- Limit Cases of the Palais-Smale Condition.

Mathematical Prerequisites.- Mathematical Prerequisites.- The Importance of the Boundary.- Vector Fields, Differential Forms, and Derivatives.- Geometry of Curves.- Motion of Curves and Solitons.- Geometry of Surfaces.- Theory of Motion of Surfaces.-...

to FPU.- Dynamics of Oscillator Chains.- Role of Chaos for the Validity of Statistical Mechanics Laws: Diffusion and Conduction.- The Fermi-Pasta-Ulam Problem and the Metastability Perspective.- Resonance, Metastability and Blow up in FPU.- Center...

This book on the state of the art in "Multifield Problems" consists of selected articles based on a conference on this topic at the University of Stuttgart in 1999. The first two articles are contributions to the general...

This unique book on the subject addresses fundamental problems and will be the standard reference for a long time to come. The authors have different scientific origins and combine these successfully, creating a text aimed at...

has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet,...

In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on...

The problem of spectral asymptotics, in particular the problem of the asymptotic dis­ tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very...

This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva­ ture -1, which is traditionally called hyperbolic 3-space. This space is the...

This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and...

This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of...

This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential...

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the...

Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields...

From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides...

This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods...

Few people outside of mathematics are aware of the varieties of mathemat­ ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and...

This book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins of the theory. Both...

In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems. This is due to the interaction of...

"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra­ jectories (generally speaking, not the individual trajectories, but ...

What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat,...

The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and...

Hysteresis effects occur in science and engineering: plasticity, ferromagnetism, ferroelectricity are well-known examples. This volume provides a self-contained and comprehensive introduction to the analysis of hysteresis...

A two-part volume containing a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications, and a detailed review of recent investigations concerning the...

This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves...

Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for...

In the Part at hand the authors undertake to give a presentation of the historical development of the theory of imbedding of function spaces, of the internal as well as the externals motives which have stimulated it, and of the...

to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra...

Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic...

Smooth ergodic theory of deterministic dynamical systems deals with the study of dynamical behaviors relevant to certain invariant measures under differentiable mappingsor ows. The relevance of invariantmeasures is that they...

Yet another introduction to rough paths.- Monotonicity of the extremal functions for one-dimensional inequalities of logarithmic Sobolev type.- Non-monotone convergence in the quadratic Wasserstein distance.- On the equation = #x002A;.- Shabat...

Flow Switchability.- Transversality and Sliding Phenomena.- A Frictional Oscillator on Time-varying Belt.- Two Oscillators with Impacts and Stick.- Dynamical Systems with Frictions.- Principles for System Interactions.

This book is primarily intended for junior-level students who take the courses on 'signals and systems'. It may be useful as a reference text for practicing engineers and scientists who want to acquire some of the concepts...

Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal...

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a...

Background and the Problem Setting.- Symplectic Reduction.- Cotangent Bundle Reduction.- The Problem Setting.- Regular Symplectic Reduction by Stages.- Commuting Reduction and Semidirect Product Theory.- Regular Reduction by Stages.- Group Extensions and...

This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building...

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...