A Dissertation For The Degree Of Master Eigenvalues Of Higher Dimensional Positive Definite Kernels

In this paper, the converging speed of eigenvalue of higher dimentional symmetric positive definite kernel is discussed. We denote by x, y the points in R, and by G the closed unit cube [0, 1]. Suppose that the kernel k Or, y) is a continuous and 1 periodic function in every variables and suppose that k Or, y) is symmetric and positive difinite on be a given integer, the symmetric derivates are also assumed to exist and to be continuous. By using the methods of Fourier series, the auxiliary operators of .K, are definited and the properties of J, and K, are also discussed. We obtain that the eigenvalues of integral operator K which is generated by k Or , y) satisfy:...