Integral Transforms, Reproducing Kernels and Their Applications
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Summary
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
Introduction
Reproducing Kernel Hilbert Spaces
Isometrical Identities and Inversion Formulas
Applications to the Approximation of Functions
Applications to Analytic Extension Formulas and Real Inversion Formulas for the Lapace Transform
Applications to Source Inverse Problems
Appendix 1: Applications to Representations of Inverse Functions
Appendix 2: Natural Norm Inequalities in Nonlinear Transforms
Appendix 3: Stability of Lipschitz Type in Determination of Initial Heat Distributions
