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This paper provides a framework for investigations in fluctuation theory forL\'evy processes with matrix-exponential jumps. We present a matrix form of thecomponents of the infinitely divisible factorization. Using this representationwe establish generalizations of some results known for compound Poissonprocesses with exponential jumps in one direction and generally distributedjumps in the other direction.

Distribution of some functionals for a L\'evy process with matrix-exponential jumps of the same sign