Integral Transforms, Reproducing Kernels and Their Applications - 9780367448233

CRC Press

This book is an essentially self-contained presentation of the theory of reproducing kernels in connection with integral transforms in the framework of Hilbert spaces. It presents a variety of concrete results of integral transforms' application for isometrical identities and inversion formulas. > 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. > 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