Abel Integral Equations

ISBN-13: 9783540536680 / Angielski / Miękka / 1991 / 222 str.

Rudolf Gorenflo; Sergio Vessella

Opis

This monograph on integral equations focuses specifically on Abel equations and their applications in such fields as spectroscopy and stereology. The text, which requires some background in functional analysis, maps the properties of Abel integral operators.

Spis treści

Basic theory and representation formulas.- Applications of Abel's original integral equation: Determination of potentials.- Applications of a transformed abel integral equation.- Smoothing properties of the abel operators.- Existence and uniqueness theorems.- Relations between abel transform and other integral transforms.- Nonlinear abel integral equations of second kind.- Illposedness and stabilization of linear abel integral equations of first kind.- On numerical treatment of first kind abel integral equations.