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

Matthias Langer, Harald Woracek

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)285-312
Number of pages28
JournalComplex Analysis and Operator Theory
Volume7
Issue number1
Early online date12 May 2011
DOIs
Publication statusPublished - Feb 2013

Keywords

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

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