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M. Langer, H. Woracek:
"The exponential type of the fundamental solution of an indefinite Hamiltonian system";
Complex Analysis and Operator Theory, 1 (2011), 28 S.

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.

Hamiltonian system, Exponential type, Pontryagin space

http://dx.doi.org/10.1007/s11785-011-0152-3