Harmonic analysis and hypergroups
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書誌事項
Harmonic analysis and hypergroups
Springer Science+Business Media, c1998
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Trends in mathematics
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注記
Includes papers presented at an International Conference on Harmonic Analysis, held Dec. 18-22, 1995 at the University of Delhi
Includes bibliographical references and index
originally published by Birkhäuser in 1998
内容説明・目次
内容説明
Under the guidance and inspiration of Dr. Ajit Iqbal Singh, an International Conference on Harmonie Analysis took place at the Uni- versity of Delhi, India, from December 18 to 22, 1995. Twenty-one dis- tinguished mathematicians from around the world, as weIl as many from India, participated in this successful and stimulating conference. An underlying theme of the conference was hypergroups, the the- ory of wh ich has developed and been found useful in fields as diverse as special functions, differential equations, probability theory, representa- tion theory, measure theory, Hopf algebras and quantum groups. Some other areas of emphasis that emerged were harmonie analysis of analytic functions, ergo die theory and wavelets. This book includes most of the proceedings of this conference. I chaired the Editorial Board for this publication; the other members were J. M. Anderson (University College London), G. L. Litvinov (Centre for Optimization and Mathematical Modeling, Institute for New Technolo- gies, Moscow), Mrs. A. I. Singh (University ofDelhi, India), V. S. Sunder (Institute of Mathematical Sciences, C.LT., Madras, India), and N. J.
Wildberger (University of New South Wales, Australia). I appreciate all the help provided by these editors as weIl as the help and cooperation of Our authors and referees of their papers. I especially appreciate techni- cial assistance and advice from Alan L. Schwartz (University of Missouri - St. Louis, USA) and Martin E. Walter (University of Colorado, USA). Finally, I thank Our editor, Ann Kostant, for her help and encouragement during this project.
目次
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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