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- catalog abstract "In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.".
- catalog contributor b3096368.
- catalog contributor b3096369.
- catalog created "c1991.".
- catalog date "1991".
- catalog date "c1991.".
- catalog dateCopyrighted "c1991.".
- catalog description "In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.".
- catalog description "Includes bibliographical references (p. [195]-209) and index.".
- catalog extent "vii, 215 p. :".
- catalog hasFormat "Abel integral equations.".
- catalog identifier "038753668X (Springer-Verlag New York Berlin Heidelberg : acid-free paper)".
- catalog identifier "354053668X (Springer-Verlag Berlin Heidelberg New York : acid-free paper) :".
- catalog isFormatOf "Abel integral equations.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1461.".
- catalog isPartOf "Lecture notes in mathematics ; 1461".
- catalog issued "1991".
- catalog issued "c1991.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Abel integral equations.".
- catalog subject "510 s 515/.45 20".
- catalog subject "Abel integral equations.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Mathematics.".
- catalog subject "Numerical analysis.".
- catalog subject "QA3 .L28 no. 1461 QA431".
- catalog title "Abel integral equations : analysis and applications / Rudolf Gorenflo, Sergio Vessella.".
- catalog type "text".