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Canonical Structures in Potential Theory is part of a two-volume set that describes a breakthrough in analytical techniques for determining diffraction from classes of canonical scatterers with edges and other complex cavity features. This volume develops the mathematics for solving mixed boundary potential problems for structures with cavities and edges. It presents groundbreaking advances and uses the Abel integral transform and the method of regularization to present a unified treatment of potential theory and diffraction. The authors also describe many applications of real physical and engineering significance and provide physical interpretation of explicit mathematical solutions.