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Harmonic Function Theory de Sheldon Axler

Harmonic Function Theory: Graduate Texts in Mathematics, cartea 137

Autor Sheldon Axler, Paul Bourdon, Ramey Wade
en Limba Engleză Paperback – 2 dec 2010
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
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Paperback (1) 42297 lei  38-44 zile
  Springer – 2 dec 2010 42297 lei  38-44 zile
Hardback (1) 57229 lei  6-8 săpt.
  Springer – 25 ian 2001 57229 lei  6-8 săpt.

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Specificații

ISBN-13: 9781441929112
ISBN-10: 1441929118
Pagini: 276
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.39 kg
Ediția:Softcover reprint of the original 2nd ed. 2001
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Graduate

Descriere

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.

Cuprins

* Basic Properties of Harmonic Functions * Bounded Harmonic Functions * Positive Harmonic Functions * The Kelvin Transform * Harmonic Polynomials * Harmonic Hardy Spaces * Harmonic Functions on Half-Spaces * Harmonic Bergman Spaces * The Decomposition Theorem * Annular Regions * The Dirichlet Problem and Boundary Behavior * Volume, Surface Area, and Integration on Spheres * Harmonic Function Theory and Mathematica * References * Symbol Index * Index

Recenzii

From the reviews of the second edition:
"There are several major changes in this second edition … . Many exercises have been added and several photographs of mathematicians related to harmonic functions are included. The book is a nice introduction to the fundamental notions of potential theory." (European Mathematical Society Newsletter, June, 2002)
"We warmly recommend this textbook to graduate students interested in Harmonic Function Theory and/or related areas. We are sure that the reader will be able to appreciate the lively and illuminating discussions in this book, and therefore, will certainly gain a better understanding of the subject." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 67, 2001)
"This is a new edition of a nice textbook … on harmonic functions in Euclidean spaces, suitable for a beginning graduate level course. … New exercises are added and numerous minor improvements throughout the text are made." (Alexander Yu. Rashkovsky, Zentralblatt MATH, Vol. 959, 2001)