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Elsevier

Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Differential Calculus and Holomorphy

    Real and Complex Analysis in Locally Convex Spaces
    • 1st Edition
    • Volume 64
    • J.F. Colombeau
    • English

  • The Inverse Scattering Transformation and The Theory of Solitons

    • 1st Edition
    • Volume 50
    • W. Eckhaus + 1 more
    • English

  • Graded Ring Theory

    • 1st Edition
    • C. Nastasescu + 1 more
    • English
    This book is aimed to be a ‘technical’ book on graded rings. By ‘technical’ we mean that the book should supply a kit of tools of quite general applicability, enabling the reader to build up his own further study of non-commutative rings graded by an arbitrary group. The body of the book, Chapter A, contains: categorical properties of graded modules, localization of graded rings and modules, Jacobson radicals of graded rings, the structure thedry for simple objects in the graded sense, chain conditions, Krull dimension of graded modules, homogenization, homological dimension, primary decomposition, and more. One of the advantages of the generality of Chapter A is that it allows direct applications of these results to the theory of group rings, twisted and skew group rings and crossed products. With this in mind we have taken care to point out on several occasions how certain techniques may be specified to the case of strongly graded rings. We tried to write Chapter A in such a way that it becomes suitable for an advanced course in ring theory or general algebra, we strove to make it as selfcontained as possible and we included several problems and exercises. Other chapters may be viewed as an attempt to show how the general techniques of Chapter A can be applied in some particular cases, e.g. the case where the gradation is of type Z. In compiling the material for Chapters B and C we have been guided by our own research interests. Chapter 6 deals with commutative graded rings of type 2 and we focus on two main topics: artihmeticallygraded domains, and secondly, local conditions for Noetherian rings. In Chapter C we derive some structural results relating to the graded properties of the rings considered. The following classes of graded rings receive special attention: fully bounded Noetherian rings, birational extensions of commutative rings, rings satisfying polynomial identities, and Von Neumann regular rings. Here the basic idea is to derive results of ungraded nature from graded information. Some of these sections lead naturally to the study of sheaves over the projective spectrum Proj(R) of a positively graded ring, but we did not go into these topics here. We refer to [125] for a noncommutative treatment of projective geometry, i.e. the geometry of graded P.I. algebras.

  • Geometry of Riemann Surfaces and Teichmüller Spaces

    • 1st Edition
    • Volume 169
    • M. Seppälä + 1 more
    • English
    The moduli problem is to describe the structure of the spaceof isomorphism classes of Riemann surfaces of a giventopological type. This space is known as the modulispace and has been at the center of pure mathematics formore than a hundred years. In spite of its age, this fieldstill attracts a lot of attention, the smooth compact Riemannsurfaces being simply complex projective algebraic curves.Therefore the moduli space of compact Riemann surfaces is alsothe moduli space of complex algebraic curves. This space lieson the intersection of many fields of mathematics and may bestudied from many different points of view.The aim of thismonograph is to present information about the structure of themoduli space using as concrete and elementary methods aspossible. This simple approach leads to a rich theory andopens a new way of treating the moduli problem, putting newlife into classical methods that were used in the study ofmoduli problems in the 1920s.

  • Nuclear and Conuclear Spaces

    • 1st Edition
    • Volume 52
    • H. Hogbe-Nlend + 1 more
    • English

  • Probabilities and Potential, B

    Theory of Martingales
    • 1st Edition
    • Volume 72
    • C. Dellacherie + 1 more
    • English

  • Weighted Norm Inequalities and Related Topics

    • 1st Edition
    • Volume 116
    • J. García-Cuerva + 1 more
    • English
    The unifying thread of this book is the topic of Weighted Norm Inequalities, but many other related topics are covered, including Hardy spaces, singular integrals, maximal operators, functions of bounded mean oscillation and vector valued inequalities. The emphasis is placed on basic ideas; problems are first treated in a simple context and only afterwards are further results examined.

  • Stochastic Control by Functional Analysis Methods

    • 1st Edition
    • Volume 11
    • A. Bensoussan
    • English

  • Foundations of Infinitesimal Stochastic Analysis

    • 1st Edition
    • K.D. Stroyan + 1 more
    • English
    This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

  • Approximation Problems in Analysis and Probability

    • 1st Edition
    • Volume 159
    • M.P. Heble
    • English
    This is an exposition of some special results on analytic or C∞-approximation of functions in the strong sense, in finite- and infinite-dimensional spaces. It starts with H. Whitney's theorem on strong approximation by analytic functions in finite-dimensional spaces and ends with some recent results by the author on strong C∞-approximation of functions defined in a separable Hilbert space. The volume also contains some special results on approximation of stochastic processes. The results explained in the book have been obtained over a span of nearly five decades.

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