Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Classical potential theory/ David H Armitage & Stephen J Gardiner

By: Contributor(s): Series: Springer Monographs in MathematicsPublication details: London: Springer, 2001Description: xvi, 333 pages, 24 cmISBN:
  • 9781852336189
Subject(s): DDC classification:
  • 23 515.9 Ar733
Contents:
1. Harmonic functions -- 2. Harmonic polynomials -- 3. Subharmonic functions -- 4. Potentials -- 5. Polar sets and capacity -- 6. The Dirichlet problem -- 7. The Fine topology -- 8. The Martin boundary -- 9. Boundary limits
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.9 Ar733 (Browse shelf(Opens below)) Available 138484
Total holds: 0

Includes bibliographical references and index

1. Harmonic functions -- 2. Harmonic polynomials -- 3. Subharmonic functions -- 4. Potentials -- 5. Polar sets and capacity -- 6. The Dirichlet problem -- 7. The Fine topology -- 8. The Martin boundary -- 9. Boundary limits

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.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in