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

Matthias Langer, Harald Woracek

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

## 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.
Original language English 285-312 28 Complex Analysis and Operator Theory 7 1 12 May 2011 https://doi.org/10.1007/s11785-011-0152-3 Published - Feb 2013

## Keywords

• Hamiltonian system
• exponential type
• Pontryagin space
• fundamental solution
• indefinite

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