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

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

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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.