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Geometric Applications of Fourier Series and Spherical Harmonics / H Groemer

By: Groemer, HContributor(s): Groemer, HMaterial type: Text

TextPublisher number: :Technical Bureau India Pvt. Ltd. | :E/261, Shastri Nagar DelhiSeries: Encyclopedia of mathematics and its applications, volume 61Publication details: New York : Cambridge University Press, ©1996Description: xi, 329p 24cmISBN: 9780521119658Subject(s): Mathematics | Analysis | Convex sets | Spherical harmonics | Séries de Fourier | Mathematics -- Calculus | Mathematics - Mathematical Analysis | Convexe verzamelingenDDC classification: 515.2433 GRO

Contents:

1. Analytic Preparations -- 2. Geometric Preparations -- 3. Fourier Series and Spherical Harmonics -- 4. Geometric Applications of Fourier Series -- 5. Geometric Applications of Spherical Harmonics.

Summary: 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. Almost all these geometric results appear here in book form for the first time. An important feature of the book is that all the necessary tools from classical theory of spherical harmonics are developed as concretely as possible, 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 characterizations 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 mathematicians.

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Holdings
Item type	Current library	Call number	Status	Notes	Date due	Barcode	Item holds
Books	SNU LIBRARY	515.2433 GRO (Browse shelf(Opens below))	Available	Books Shifted in Mathematics Dept.
Books	SNU LIBRARY	515.2433 GRO (Browse shelf(Opens below))	Not For Loan			28586

Total holds: 0

1. Analytic Preparations --
2. Geometric Preparations --
3. Fourier Series and Spherical Harmonics --
4. Geometric Applications of Fourier Series --
5. Geometric Applications of Spherical Harmonics.

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. Almost all these geometric results appear here in book form for the first time. An important feature of the book is that all the necessary tools from classical theory of spherical harmonics are developed as concretely as possible, 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 characterizations 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 mathematicians.

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