Theory of Reproducing Kernels and Applications

1. Definitions and Examples of Reproducing Kernel Hilbert Spaces
Saburou Saitoh, Yoshihiro Sawano

2. Fundamental Properties of RKHS
Saburou Saitoh, Yoshihiro Sawano

3. Moore Penrose Generalized Inverses and Tikhonov Regularization
Saburou Saitoh, Yoshihiro Sawano

4. Real Inversion Formulas of the Laplace Transform
Saburou Saitoh, Yoshihiro Sawano

5. Applications to Ordinary Differential Equations
Saburou Saitoh, Yoshihiro Sawano

6. Applications to Partial Differential Equations
Saburou Saitoh, Yoshihiro Sawano

7. Applications to Integral Equations
Saburou Saitoh, Yoshihiro Sawano

8. Special Topics on Reproducing Kernels
Saburou Saitoh, Yoshihiro Sawano

Keywords: Mathematics, Functional Analysis, Fourier Analysis, Functions of a Complex Variable, Partial Differential Equations