Theory of Reproducing Kernels and Applications

• Main Authors: Saitoh, Saburou (Author), Sawano, Yoshihiro (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2016.
• Series: Developments in Mathematics, 44
• Subjects: Mathematics.; Fourier analysis.; Functional analysis.; Functions of complex variables.; Partial differential equations.; Functional Analysis.; Fourier Analysis.; Functions of a Complex Variable.; Partial Differential Equations.

This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications. In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of repr...

Table of Contents:

• Definitions and examples of reproducing kernel Hilbert spaces
• Fundamental properties of RKHS
• Moore Penrose generalized inverses and Tikhonov regularization
• Real inversion formulas of the Laplace transform
• Applications to ordinary differential equations
• Applications to partial differential equations
• Applications to integral equations
• Special topics on reproducing kernels
• Appendices
• Index.