ABSTRACT
On the one hand there is a great variety of challenging applications. O'Sullivan (1986) mentions areas like crystallography, geophysics, medical electrocardiograms, meteorology, microftuoroimagery, radio astronomy, reservoir engineering, and tomography. To this list one might add instances of physical systems like inverse heat conduction, Mair and Ruymgaart ( 1996), and imaging. Some of these examples will be considered more closely in this chapter. On the other hand there are many ramifications in other areas of mathematics such as operator theory, harmonic analysis, numerical analysis, and approximation theory. A recent survey of mathematical methodology is given by Bertero (1989); see also Kress (1989) for a recent monograph on integral equations.
