Classical Potential Theory (Springer Monographs in Mathematics)

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Item specifics

Condition
Good
A book that has been read but is in good condition. Very minimal damage to the cover including scuff marks, but no holes or tears. The dust jacket for hard covers may not be included. Binding has minimal wear. The majority of pages are undamaged with minimal creasing or tearing, minimal pencil underlining of text, no highlighting of text, no writing in margins. No missing pages. See the seller’s listing for full details and description of any imperfections. See all condition definitionsopens in a new window or tab
Seller Notes
“Clean text. Slight smoke smell.”
ISBN
9781852336189
Subject Area
Mathematics
Publication Name
Classical Potential Theory
Publisher
Springer London, The Limited
Item Length
9.3 in
Subject
General, Vector Analysis, Complex Analysis, Mathematical Analysis
Publication Year
2000
Series
Springer Monographs in Mathematics Ser.
Type
Textbook
Format
Hardcover
Language
English
Item Height
0.4 in
Author
David H. Armitage, Stephen J. Gardiner
Item Weight
52.6 Oz
Item Width
6.1 in
Number of Pages
Xvi, 333 Pages
Category

About this product

Product Identifiers

Publisher
Springer London, The Limited
ISBN-10
1852336188
ISBN-13
9781852336189
eBay Product ID (ePID)
1805150

Product Key Features

Number of Pages
Xvi, 333 Pages
Publication Name
Classical Potential Theory
Language
English
Subject
General, Vector Analysis, Complex Analysis, Mathematical Analysis
Publication Year
2000
Type
Textbook
Author
David H. Armitage, Stephen J. Gardiner
Subject Area
Mathematics
Series
Springer Monographs in Mathematics Ser.
Format
Hardcover

Dimensions

Item Height
0.4 in
Item Weight
52.6 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
00-056312
Dewey Edition
21
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515.9
Table Of Content
1. Harmonic Functions.- 1.1. Laplace's equation.- 1.2. The mean value property.- 1.3. The Poisson integral for a ball.- 1.4. Harnack's inequalities.- 1.5. Families of harmonic functions: convergence properties.- 1.6. The Kelvin transform.- 1.7. Harmonic functions on half-spaces.- 1.8. Real-analyticity of harmonic functions.- 1.9. Exercises.- 2. Harmonic Polynomials.- 2.1. Spaces of homogeneous polynomials.- 2.2. Another inner product on a space of polynomials.- 2.3. Axially symmetric harmonic polynomials.- 2.4. Polynomial expansions of harmonic functions.- 2.5. Laurent expansions of harmonic functions.- 2.6. Harmonic approximation.- 2.7. Harmonic polynomials and classical polynomials.- 2.8. Exercises.- 3. Subharmonic Functions.- 3.1. Elementary properties.- 3.2. Criteria for subharmonicity.- 3.3. Approximation of subharmonic functions by smooth ones.- 3.4. Convexity and subharmonicity.- 3.5. Mean values and subharmonicity.- 3.6. Harmonic majorants.- 3.7. Families of subharmonic functions: convergence properties.- 3.8. Exercises.- 4. Potentials.- 4.1. Green functions.- 4.2. Potentials.- 4.3. The distributional Laplacian.- 4.4. The Riesz decomposition.- 4.5. Continuity and smoothness properties.- 4.6. Classical boundary limit theorems.- 4.7. Exercises.- 5. Polar Sets and Capacity.- 5.1. Polar sets.- 5.2. Removable singularity theorems.- 5.3. Reduced functions.- 5.4. The capacity of a compact set.- 5.5. Inner and outer capacity.- 5.6. Capacitable sets.- 5.7. The fundamental convergence theorem.- 5.8. Logarithmic capacity.- 5.9. Hausdorff measure and capacity.- 5.10. Exercises.- 6. The Dirichlet Problem.- 6.1. Introduction.- 6.2. Upper and lower PWB solutions.- 6.3. Further properties of PWB solutions.- 6.4. Harmonic measure.- 6.5. Negligible sets.- 6.6. Boundarybehaviour.- 6.7. Behaviour near infinity.- 6.8. Regularity and the Green function.- 6.9. PWB solutions and reduced functions.- 6.10. Superharmonic extension.- 6.11. Exercises.- 7. The Fine Topology.- 7.1. Introduction.- 7.2. Thin sets.- 7.3. Thin sets and reduced functions.- 7.4. Fine limits.- 7.5. Thin set s and the Dirichlet problem.- 7.6. Thinness at infinity.- 7.7. Wiener' s criterion.- 7.8. Limit properties of superharmonic functions.- 7.9. Harmonic approximation.- 8. The Martin Boundary.- 8.1. The Martin kernel and Mart in boundary.- 8.2. Reduced functions and minimal harmonic functions.- 8.3. Reduction ?0s and ?1.- 8.4. The Martin representation.- 8.5. The Martin boundary of a strip.- 8.6. The Martin kernel and the Kelvin transform.- 8.7. The boundary Harnack principle for Lipschitz domains.- 8.8. The Marti n boundary of a Lipschitz domain.- 9. Boundary Limits.- 9.1. Swept measures and the Dirichlet problem for the Martin compactification.- 9.2. Minimal thinness.- 9.3. Minimal fine limits.- 9.4. The Fatou-Naïm-Doob theorem.- 9.5. Minimal thinness in subdomains.- 9.6. Refinements of limit theorems.- 9.7. Minimal thinness in a half-space.- Historical Notes.- References.- Symbol Index.
Synopsis
A long-awaited, updated introductory text by the world leaders in potential theory. This essential reference work covers all aspects of this major field of mathematical research, from basic theory and exercises to more advanced topological ideas. The largely self-contained presentation makes it basically accessible to graduate students., From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises. The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine topology, the Martin boundary and minimal thinness. The presentation is largely self-contained and is accessible to graduate students, the only prerequisites being a reasonable grounding in analysis and several variables calculus, and a first course in measure theory. The book will prove an essential reference to all those with an interest in potential theory and its applications.
LC Classification Number
QA331.7

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