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Functional Equations in Several Variables

$233.00

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 1989
  • availability: Available
  • format: Hardback
  • isbn: 9780521352765

$233.00
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About the Authors
  • Deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioral, and social sciences. The authors emphasize applications, although not at the expense of theory, and have kept the prerequisites to a minimum; the reader should be familiar with calculus and some simple structures of algebra and have a basic knowledge of Lebesque integration. For the applications the authors have included references and explained the results used. The book is designed so that the chapters may be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. Each chapter concludes with exercises and further results, 400 in all, which extend and test the material presented in the text. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography of over 1600 items. This volume will be of interest to professionals and graduate students in pure and applied mathematics.

    Reviews & endorsements

    "The book has been designed so that the chapters can be read almost independently of each other. This beautifully written treatise is very useful as a reference book for research workers in the area." Mathematical Reviews

    "...this is an excellent reference book, in general, for senior and higher level physics students, and perhaps for numerical analysts working on computer algorithms....I would not hesitate to recommend this book to any physics and geophysics graduate students, as well as to some interested faculty members." Physics in Canada

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    Product details

    • Date Published: April 1989
    • format: Hardback
    • isbn: 9780521352765
    • length: 480 pages
    • dimensions: 234 x 156 x 27 mm
    • weight: 0.85kg
    • availability: Available
  • Table of Contents

    Preface
    Further information
    1. Axiomatic motivation of vector addition
    2. Cauchy's equation: Hamel basis
    3. Three further Cauchy equations: an application to information theory
    4. Generalizations of Cauchy's equations to several multiplace vector and matrix functions: an application to geometric objects
    5. Cauchy's equations for complex functions: applications to harmonic analysis and to information measures
    6. Conditional Cauchy equations: an application to geometry and a characterization of the Heaviside functions
    7. Addundancy, extensions, quasi-extensions and extensions almost everywhere: applications to harmonic analysis and to rational decision making
    8. D'Alembert's functional equation: an application to noneuclidean mechanics
    9. Images of sets and functional equations: applications to relativity theory and to additive functions bounded on particular sets
    10. Some applications of functional equations in functional analysis, in the geometry of Banach spaces and in valauation theory
    11. Characterizations of inner product spaces: an application to gas dynamics
    12. Some related equations and systems of equations: applications to combinatorics and Markov processes
    13. Equations for trigonometric and similar functions
    14. A class of equations generalizing d'Alembert and Cauchy Pexider-type equations
    15. A further generalization of Pexider's equation: a uniqueness theorem: an application to mean values
    16. More about conditional Cauchy equations: applications to additive number theoretical functions and to coding theory
    17. Mean values, mediality and self-distributivity
    18. Generalized mediality: connection to webs and nomograms
    19. Further composite equations: an application to averaging theory
    20. Homogeneity and some generalizations: applications to economics
    21. Historical notes
    Notations and symbols
    Hints to selected 'exercises and further results'
    Bibliography
    Author index
    Subject index.

  • Authors

    J. Aczel, University of Waterloo, Ontario

    J. Dhombres, Université de Nantes, France

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