ENGLISH

Abel Integral Equations: Analysis and Applications

By Rudolf Gorenflo , Sergio Vessella (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1991
ISBN
9780387536682, 0-387-53668-X, 354053668X
DOI
10.1007/BFb0084665
LCC
QA3 .L28 no. 1461,QA431 .L28 no. 1461
Open Library ID
OL2029094M
Language
english
Format
DJVU
Filesize
1 MB (1295421 bytes)
Series
Lecture Notes in Mathematics 1461
Edition
1
Pages
222\224
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11
Analysis; Numerical Analysis

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.

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