M. Langer and H. Woracek,
The exponential type of the fundamental solution of an indefinite Hamiltonian system,
Complex Anal. Oper. Theory 7 (2013), 285–312
Abstract:
The fundamental solution of a Hamiltonian system whose Hamiltonian H
is positive definite and locally integrable is an entire function of exponential type.
Its exponential type can be computed as the integral over √(det H).
We show that this formula remains true in the indefinite (Pontryagin space) situation,
where the Hamiltonian is permitted to have finitely many inner singularities.
As a consequence, we obtain a statement on non-cancellation of exponential growth
for a class of entire matrix functions.