Geometric applications of Fourier series and spherical harmonics / H. Groemer.

By:

Groemer, H

Material type: Text

TextSeries: Encyclopedia of mathematics and its applications ; volume 61.Publisher: Cambridge ; New York : Cambridge University Press, [1996]Copyright date: ©1996Description: 1 online resource (xi, 329 pages)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781107088818
110708881X

Subject(s): Genre/Form:

Electronic books.

Additional physical formats: Print version:: Geometric applications of Fourier series and spherical harmonicsDDC classification:

515/.2433 22

LOC classification:

QA640 .G76 1996eb

Other classification:

31.35

Online resources:

Click here to access online

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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Item type	Home library	Collection	Call number	Materials specified	Status	Date due	Barcode
Electronic-Books	OPJGU Sonepat- Campus	E-Books EBSCO			Available

Includes bibliographical references (pages 311-318) and indexes.

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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