The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Table of Contents
1. Introduction 2. Reproducing kernel Hilbert spaces 3. Isometrical identities and inversion formulas 4. Applications to the approximation of functions 5. Applications to analytic extension formulas and real inversion formulas for the Laplace transform 6. Applications to source inverse problems