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On the Helmholtz operator for Euler morphisms

Published online by Cambridge University Press:  27 August 2003

IVAN KOLÁŘ  and
RAFFAELE VITOLO
IVAN KOLÁŘ
Affiliation:
Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, 66295 Brno, Czech Republic. e-mail: kolar@math.muni.cz
RAFFAELE VITOLO
Affiliation:
Department of Mathematics “E. De Giorgi”, University of Lecce, Via per Arnesano, 73100 Lecce, Italy. e-mail: raffaele.vitolo@unifi.it
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Abstract

The variational sequence describes the Helmholtz conditions for local variationality in terms of the Helmholtz map, which is defined on a factor space. We study a tensor modification of this construction and characterize a unique representative, which is called the Helmholtz operator. For the first and the second order cases we prove that, up to a multiplicative constant, the Helmholtz operator is the unique natural operator of the type in question.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 2 , September 2003 , pp. 277 - 290
Copyright
2003 Cambridge Philosophical Society

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