Distribution of some functionals for a Lévy process with matrix-exponential jumps of the same sign

This paper provides a framework for investigations in fluctuation theory for Lévy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we establish generalizations of some results known for compound Poisson processes with exponential jumps in one direction and generally distributed jumps in the other direction.