We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the weight is variable. Obviously, this new method will generalize a number of applications of reproducing kernel theory to many areas.
Er Gao. Songhe Song. Xinjian Zhang. "Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral." J. Appl. Math. 2012 1 - 13, 2012. https://doi.org/10.1155/2012/175292