Some recursion relations for solutions of a class of equations
This work presents some recursion relations for solutions of a class of singular partial differential equations. The equations consist of iterated differential operators each of which involves real parameters.
On the solutions of some classes of PDE with singular coefficients
ABSTRACT We consider the linear Cauchy problem with analytic data for two models of second order operators with singular coefficients. We show that the propagation of the singularities of the coefficients of the subprincipal part of the operators generate singularities on the union of the characteristic surfaces, on the surfaces , and on the characteristic cone too.
Birth-death processes with killing
The purpose of this note is to point out that Karlin and McGregor's integral representation for the transition probabilities of a birth-death process on a semi-infinite lattice with an absorbing bottom state remains valid if one allows the possibility of absorption into the bottom state from any other state. Conditions for uniqueness of the minimal transition function are also given.