Harmonic Analysis and Hypergroups

Harmonic Analysis and Hypergroups

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An underlying theme in this text is the notion of hypergroups, the theory of which has been developed and used in fields as diverse as special functions, differential equations, probability theory, representation theory, measure theory, Hopf algebras, and quantum groups. Other topics include the harmonic analysis of analytic functions, ergodic theory and wavelets. The text should be a useful resource for mathematicians and graduate students who are working in the pure as well as applied areas of harmonic analysis.

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Product details

  • Hardback | 249 pages
  • 165.1 x 247.65 x 19.05mm | 520g
  • Secaucus, United States
  • English
  • 1997 ed.
  • biography
  • 0817639438
  • 9780817639433

Table of contents

Contents Preface 1 Introduction 1 The Set N of Natural Numbers 2 The Set Q of Rational Numbers 3 The Set R of Real Numbers 4 The Completeness Axiom 5 The Symbols + and - 6 * A Development of R 2 Sequences 7 Limits of Sequences 8 A Discussion about Proofs 9 Limit Theorems for Sequences 10 Monotone Sequences and Cauchy Sequences 11 Subsequences 12 limsup's and liminf's 13 * Some Topological Concepts in Metric Spaces 14 Series 15 Alternating Series and Integral Tests 16 * Decimal Expansions of Real Numbers 3 Continuity 17 Continuous Functions 18 Properties of Continuous Functions 19 Uniform Continuity 20 Limits of Functions 21 * More on Metric Spaces: Continuity 22 * More on Metric Spaces: Connectedness 4 Sequences and Series of Functions 23 Power Series 24 Uniform Convergence 25 More on Uniform Convergence 26 Differentiation and Integration of Power Series 27 * Weierstrass's Approximation Theorem 5 Differentiation 28 Basic Properties of the Derivative 29 The Mean Value Theorem 30 * L'Hospital's Rule 31 Taylor's Theorem 6 Integr ation 32 The Riemann Integral 33 Properties of the Riemann Integral 34 Fundamental Theorem of Calculus 35 * Riemann-Stieltjes Integrals 36 * Improper Integrals 37 * A Discussion of Exponents and Logarithms Appendix on Set Notation Selected Hints and Answers References Index

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