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