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M. Langer, H. Woracek:
"The exponential type of the fundamental solution of an indefinite Hamiltonian system";
in: "ASC Report 30/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

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 pdetH. 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://www.asc.tuwien.ac.at/preprint/2010/asc30x2010.pdf