Abel Integral Equations: Analysis and Applications

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In many fields of mathematical application, progress is dependent upon the flow of information between theoretical mathematicians looking for applications, mathematicians in need of theory, and scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate sources of information regarding integral equations. In the first three chapters, applications of Abel integral equations are surveyed, including determination of potentials, stereology, seismic travel times, spectroscopy and optical fibres. Subsequent chapters, which require some background in functional analysis, map properties of Abel integral operators and their relation to other integral transforms in various function spaces. Numerical methods are described, and issues concerning the existence and uniqueness of solutions of linear and nonlinear Abel integral equations are explored.