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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 scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures. ... Read more

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The volume comprises eleven survey papers based on survey lectures delivered at the Conference in Prague in July 1987, which covered various facets of potential theory, including its applications in other areas. The survey papers deal with both classical and abstract potential theory and its relations to partial differential equations, stochastic processes and other branches such as numerical analysis and topology. A collection of problems from potential theory, compiled on the occasion of the conference, is included, with additional commentaries, in the second part of this volume. ... Read more

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The text of this book comprises a thorough and detailed exposition of the mathematical theory of potential and its application to classical electromagnetic field theory. In as much as a prior knowledge of little more than vector addition and multiplication is assumed on the part of the reader, selected portions are suitable as an undergraduate text in vector analysis; at the same time the level of development is such that it may serve as a text for advanced graduate students, teachers and all professionally mature researchers in the areas of communication electromagnetics, plasma physics, electromagnetic compatability, magnetics and geomagnetism. And for students, teachers and all professionals concerned with the foundations of classical electromagnetic theory as embodied in the Maxwell-Lorentz equations, the work offers a novel approach and logical development free from many of the difficulties inherent in the conventional treatment. Over 400 exercises of varying degrees of difficulty are spread throughout the text. ... Read more

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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 potential theory, L(p)-capacity theory, fine limits of the Nagel-Stein boundary limit theorem and integrability of superharmonic functions. The notes are written for an audience familiar with the theory of integration, distributions and basic functional analysis. ... Read more

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This volume of the Encyclopaedia contains four parts each ofwhich being an informative survey of a topic in the field ofseveral complex variables. Thefirst deals with residuetheory and its applications to integrals depending onparameters, combinatorial sums and systems of algebraicequations. The second part contains recent results incomplex potential theory and the third part treats functiontheory in the unit ball covering research of the last twentyyears. The latter part includes an up-to-date account ofresearch related to a list of problems, which was publishedby Rudin in 1980.The last part of the book treats complex analysis in thefuturetube. The future tube is an important concept inmathematical physics,especially in axiomatic quantum fieldtheory, and it is related to Penrose'swork on "the complexgeometry of the real world".Researchers and graduate students in complex analysis andmathematical physics will use thisbook as a reference andas a guide to exciting areas of research. ... Read more

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This book introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Discussion includes behaviours of the scalar and vector potential and the nature of the solutions of these boundary value problems, along with the use of complex variables and conformal transformation, Green's theorem, Green's formula and Green's functions.