The exponential type of the fundamental solution of an indefinite Hamiltonian system

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Langer, Matthias and Woracek, Harald (2013) The exponential type of the fundamental solution of an indefinite Hamiltonian system. Complex Analysis and Operator Theory, 7 (1). pp. 285-312. ISSN 1661-8254 (https://doi.org/10.1007/s11785-011-0152-3)

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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 $\sqrt{det H}$. 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.

ORCID iDs

Langer, Matthias ORCID logoORCID: https://orcid.org/0000-0001-8813-7914 and Woracek, Harald;
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