Solutions for the Case of Spectrally Separable Kernel Matrices in the Probabilistic Evolution Theory (PREVTH)

Abstract: This work seeks the possibility of rather simple structures in the applications of the probabilistic evolution theory (PREVTH). We focus on the rather simple forms of the kernel matrix of the system under consideration. Such that for some specific initial vector forms the imaging under the kernel matrix produces an output proportional to the original initial vector. By using this specific kernel matrix forms we have proven that the initial direction is conserved during the evolution. However the magnitude of the solution temporally changes. As we have found these changes may remain in finite domains of the relevant axis while there is also possibilities approaching to infinity.