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Foundations of Potential Theory
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by
Oliver D Kellogg
Systematic mathematical treatment of potential theory. Knowledge of partial derivatives and multiple and line integrals assumed.
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Potential Theory in Gravity and Magnetic Applications
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by
Richard J Blakely
This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The ...
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Harmonic Measure
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by
John B Garnett, Donald E Marshall
During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback ...
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Classical Potential Theory and Its Probabilistic Counterpart
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by
Doob
From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of ...
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An introduction to the theory of Newtonian attraction
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by
A S Ramsey
An Introduction to the Theory of Newtonian Attraction BY A. S. RAMSEX M. A. FELLOW OP MAGDALENE COLLEGE, CAMBRIDGE, FORMERLY UNIVERSITY LECTURER IN MATHEMATICS Rationein vero harum Gravitatis propnetaturn, ex Phanomenis nondumpotui deducere, Hypotheses non Jingo. NEWTON CAMBRIDGE AT THE UNIVERSITY PRESS 1940 PRINTED TS GREAT BRITAIN PREFACE This ...
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Mathematical Papers
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by
George Green, N M Ferrers (Editor)
Best known for Green's theorem, George Green (1793-1841) also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works, including "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism," "Mathematical ...
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Potential Theory in the Complex Plane
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by
Ransford
Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This ...
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Method of Difference Potentials and Its Applications
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by
V S Riaben'kii, Viktor S Ryaben'kii, N K Kulman (Translator)
The book presents the method of difference potentials first proposed by the author in 1969 and contains illustrative examples and new algorithms for solving applied problems of gas dynamics, diffraction, scattering theory, and active noise screening. The fundamentals of the method are described in Parts I-III and its applications in Parts IV-VIII. ...
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Multiscale Potential Theory: With Applications to Geoscience
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by
Willi Freeden, Volker Michels
This self-contained book provides a basic foundation for students, practitioners, and researchers interested in some of the diverse new areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled and analyzed using a continuous flow of observations from ...
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Determining Spectra in Quantum Theory
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by
Maddaly Krishna, Michael Demuth
The spectral theory of Schrodinger operators, in particular those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory of selfadjoint operators in order to identify the spectrum and its components a la Lebesgue decomposition. It contains a well-developed ...
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Nonlinear potential theory of degenerate elliptic equations
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by
Juha Heinonen, Tero Kilpelainen, Olli Martio
This volume provides a detailed introduction to the nonlinear potential theory based on supersolutions to certain degenerate elliptic equations of the p-Laplacian type. Recent research has shown that such classical notions as blayage, polar sets, Perron's method and fine topology have their proper analogues in a nonlinear setting, and a coherent ...
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Harmonic Analysis and Discrete Potential Theory
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by
Massimo A Picardello
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Canonical Problems in Scattering and Potential Theory Part 1: Canonical Structures in Potential Theory
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Sergey S Vinogradov, Paul Denis Smith, E D Vinogradova
Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical ...
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Invariant Potential Theory in the Unit Ball of Cn
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by
Manfred Stoll, J W S Cassels (Editor), N J Hitchin (Editor)
This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson-Szego integrals on the ball, the Green's function for D and the Riesz decomposition theorem for ...
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Markov processes and potential theory
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by
Robert McCallum Blumenthal, R. K. Getoor
This graduate-level text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Topics include Markov processes, excessive functions, multiplicative functionals and subprocesses, and additive functionals and their potentials. A concluding chapter examines dual ...
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Chemical Applications of Atomic and Molecular Electrostatic Potentials, Reactivity, Structure, Scattering, and Energetics of Organic, Inorganic, and Biological Systems
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by
Peter Politzer, Donald G Truhlar (Editor)
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Canonical Problems in Scattering and Potential Theory Part II: Acoustic and Electromagnetic Diffraction by Canonical Structures
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by
Sergey S Vinogradov, Paul Denis Smith, E D Vinogradova
Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical ...
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Approximation, Complex Analysis, and Potential Theory
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by
Norair Arakelian (Editor), Paul M Gauthier (Editor)
Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish ...
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The Cauchy Transform, Potential Theory and Conformal Mapping
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by
Steven Robert Bell, Bell R Bell
The Cauchy integral formula is the most central result in all of classical function theory. A recent discovery of Kerzman and Stein allows more theorems than ever to be deduced from simple facts about the Cauchy integral. In this book, the Riemann Mapping Theorem is deduced, the Dirichlet and Neumann problems for the Laplace operator are solved, ...
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Potential Theory and Degenerate Partial Differential Operators
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by
Marco Biroli (Editor)
This work discusses the blending of potential theory, probability and degenerate partial differential operators. The theory of Dirichlet (Markovian) which forms on an abstract finite or infinite-dimensional space is common to all three disciplines and is investigated here.
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Potential Theory and Right Processes
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by
Lucian Beznea, NICU Boboc
This book develops the potential theory starting from a sub-Markovian resolvent of kernels on a measurable space, covering the context offered by a right process with general state space. It turns out that the main results from the classical cases (e.g., on locally compact spaces, with Green functions) have meaningful extensions to this setting. ...
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Potential Theory on Infinite Networks
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by
Paolo M Soardi
The aim of this text is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. ...
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Function Spaces and Potential Theory
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by
David R Adams
The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functions whose gradients are square integrable. More ...
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Potential Theory - Selected Topics
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by
Hiroaki Aikawa, Matts Essen
The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis. Topics covered in the book include minimal thinness, quasiadditivity of capacity, applications of singular integrals to ...
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Classical Potential Theory
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by
David H Armitage, Stephen J Gardiner
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 ...
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