The new books are available Dec. 2021 – Jan. 2022 and consist of many source programs as well as math propositions.

Chapter 1 Positive Definite Kernel
1.1 Positive-definiteness of matrix
1.2 kernel
1.3 Positive Definite Kernel
1.4 Probability
1.5 Boxner's theorem
1.6 string, tree, kernel kernel

Chapter 2 Hilbert space
2.1 Metric space and completeness
2.2 Linear space and inner product space
2.3 Hilbert space
2.4 Projection theorem
2.5 Linear operator
2.6 Compact operator

Chapter 3 Reproducing Kernel Hilbert Space
3.1 RKHS
3.2 Sobolev space
3.3 Mercer's theorem

Chapter 4 Kernel Calculation
4.1 Kernel ridge regression
4.2 Kernel analysis
4.3 Kernel SVM
4.4 Splines
4.5 Random Fourier function
4.6 Nistrom approximation
4.7 Cholesky decomposition

Chapter 5 MMD and HSIC
5.1 RKHS random variables
5.2 MMD and the two sample problem
5.3 Testing Independence via  HSIC
5.4 Kernel Kernel and Universal Kernel
5.5 Introduction to Experience Process

Chapter 6 Gauss Individual and Functional data Analysis
6.1 Regression
6.2 Classification
6.3 Auxiliary variable method
6.4 Karhunen-Loeve expansion
6.5 Functional data analysis