Reproducing Kernel for $D^2(\Omega,\rho)$ and Metric Induced by Reproducing Kernel

Abstract:

      important property of the reproducing kernel of $D^2(\Omega,\rho)$ is obtained and the reproducing kernels for $D^2(\Omega,\rho)$ are calculated when $\Omega=B_n\times B_n$ and $\rho$ are some special functions. A reproducing kernel is used to construct a semi-positive definite matrix and a distance function defined on $\Omega \times\Omega$. An inequality is obtained about the distance function and the pseudo-distance induced by the matrix.