Abel Integral Equations: Analysis and Applications [1 ed.] 9780387536682, 0-387-53668-X, 354053668X
In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i
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English Pages 222 [224] Year 1991
Table of contents :
Introduction....Pages 1-7
Basic theory and representation formulas....Pages 8-25
Applications of Abel's original integral equation: Determination of potentials....Pages 26-34
Applications of a transformed abel integral equation....Pages 35-63
Smoothing properties of the abel operators....Pages 64-82
Existence and uniqueness theorems....Pages 83-94
Relations between abel transform and other integral transforms....Pages 95-128
Nonlinear abel integral equations of second kind....Pages 129-153
Illposedness and stabilization of linear abel integral equations of first kind....Pages 154-181
On numerical treatment of first kind abel integral equations....Pages 182-194
Introduction....Pages 1-7
Basic theory and representation formulas....Pages 8-25
Applications of Abel's original integral equation: Determination of potentials....Pages 26-34
Applications of a transformed abel integral equation....Pages 35-63
Smoothing properties of the abel operators....Pages 64-82
Existence and uniqueness theorems....Pages 83-94
Relations between abel transform and other integral transforms....Pages 95-128
Nonlinear abel integral equations of second kind....Pages 129-153
Illposedness and stabilization of linear abel integral equations of first kind....Pages 154-181
On numerical treatment of first kind abel integral equations....Pages 182-194
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