Harmonic function theory / Sheldon Axler, Paul Bourdon, Wade Ramey.

Format:

Book

Author/Creator:

Axler, Sheldon Jay.

Contributor:

Bourdon, Paul.

Ramey, Wade.

Series:

Graduate texts in mathematics ; 137.

Graduate texts in mathematics ; 137

Language:

English

Subjects (All):

Harmonic functions.

Physical Description:

xi, 259 pages : illustrations ; 25 cm.

Edition:

Second edition.

Place of Publication:

New York : Springer, [2001]

Summary:

This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher?'s Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by email-supplements the text for readers who wish to explore harmonic function theory on a computer.

Notes:

Includes bibliographical references (pages 249-250) and indexes.

ISBN:

0387952187

OCLC:

45315455