Sheldon Axler

Harmonic Function Theory - Graduate Texts in Mathematics Sheldon Axler Softcover Reprint of the Original 2nd Ed. 2001 edition

Description for Sales People: 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 new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, aa 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. Review Quotes: 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 M ricz, 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.gReview Quotes: 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 Moricz, 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) Table of Contents: * 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 * IndexReview Quotes: 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 Moricz, 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)"Publisher Marketing: This text looks at about harmonic functions in Euclidean space. The new edition contains a 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.

Contributor Bio:  Axler, Sheldon Axler-San Francisco State University