Q-matrices as pseudo-differential operators with negative definite symbols


  • Dedicated to Professor Hans Triebel on the occasion of his 75th birthday


Operators induced by Q-matrices on equation image are shown to satisfy the positive maximum principle and to have a representation as a pseudo-differential operator with symbol equation image which is with respect to the co-variable negative definite (in the sense of Schoenberg). This observation leads already towards a more geometric interpretation of the transition matrix of the associated Markov chain.