Geometric applications of Fourier series and spherical harmonics

H. Groemer

This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

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[目次]

  • Preface
  • 1. Analytic preparations
  • 2. Geometric preparations
  • 3. Fourier series and spherical harmonics
  • 4. Geometric applications of Fourier series
  • 5. Geometric applications of spherical harmonics
  • References
  • List of symbols
  • Author index
  • Subject index.

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この本の情報

書名 Geometric applications of Fourier series and spherical harmonics
著作者等 Groemer, H.
Groemer Helmut
シリーズ名 Encyclopedia of mathematics and its applications
出版元 Cambridge University Press
刊行年月 1996
ページ数 xi, 329 p.
大きさ 24 cm
ISBN 9780521473187
NCID BA28606172
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言語 英語
出版国 イギリス
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