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- catalog abstract "Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.".
- catalog contributor b11977280.
- catalog contributor b11977281.
- catalog contributor b11977282.
- catalog created "2001.".
- catalog date "2001".
- catalog date "2001.".
- catalog dateCopyrighted "2001.".
- catalog description "Ch. 1. Basic Properties of Harmonic Functions -- Ch. 2. Bounded Harmonic Functions -- Ch. 3. Positive Harmonic Functions -- Ch. 4. The Kelvin Transform -- Ch. 5. Harmonic Polynomials -- Ch. 6. Harmonic Hardy Spaces -- Ch. 7. Harmonic Functions on Half-Spaces -- Ch. 8. Harmonic Bergman Spaces -- Ch. 9. The Decomposition Theorem -- Ch. 10. Annular Regions -- Ch. 11. The Dirichlet Problem and Boundary Behavior -- App. A. Volume, Surface Area, and Integration on Spheres -- App. B. Harmonic Function Theory and Mathematica.".
- catalog description "Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.".
- catalog description "Includes bibliographical references (p. 249-250) and indexes.".
- catalog description "Includes bibliographical references and indexes.".
- catalog extent "xi, 259 p. :".
- catalog identifier "0387952187 (alk. paper)".
- catalog isPartOf "Graduate texts in mathematics ; 137".
- catalog issued "2001".
- catalog issued "2001.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "515/.53 21".
- catalog subject "Harmonic functions.".
- catalog subject "Mathematics.".
- catalog subject "Potential theory (Mathematics).".
- catalog subject "QA405 .A95 2001".
- catalog tableOfContents "Ch. 1. Basic Properties of Harmonic Functions -- Ch. 2. Bounded Harmonic Functions -- Ch. 3. Positive Harmonic Functions -- Ch. 4. The Kelvin Transform -- Ch. 5. Harmonic Polynomials -- Ch. 6. Harmonic Hardy Spaces -- Ch. 7. Harmonic Functions on Half-Spaces -- Ch. 8. Harmonic Bergman Spaces -- Ch. 9. The Decomposition Theorem -- Ch. 10. Annular Regions -- Ch. 11. The Dirichlet Problem and Boundary Behavior -- App. A. Volume, Surface Area, and Integration on Spheres -- App. B. Harmonic Function Theory and Mathematica.".
- catalog title "Harmonic function theory / Sheldon Axler, Paul Bourdon, Wade Ramey.".
- catalog type "text".