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Proceedings of the London Mathematical Society Advance Access originally published online on July 17, 2007
Proceedings of the London Mathematical Society 2007 95(3):687-708; doi:10.1112/plms/pdm025
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© 2007 London Mathematical Society

Uniqueness theorems for (sub-)harmonic functions with applications to operator theory

Alexander Borichev

Centre de Mathématiques et Informatique
Université d'Aix-Marseille I
39 rue Frédéric Joliot-Curie
13453 Marseille
France
borichev{at}cmi.univ-mrs.fr

Ralph Chill

Université Paul Verlaine–Metz et CNRS
Laboratoire de Mathématiques et Applications de Metz
UMR 7122
Bât. A, Ile du Saulcy
57045 Metz cedex 1
France

Yuri Tomilov

Faculty of Mathematics and Computer Science
Nicolas Copernicus University
ul. Chopina 12/18
87-100 Torun
Poland
tomilov{at}mat.uni.torun.pl

Received 21 September 2006. Revision received 16 February 2007.

We obtain uniqueness theorems for harmonic and subharmonic functions of a new type. They lead to new analytic extension criteria and new conditions for stability of operator semigroups in Banach spaces with Fourier type.

2000 Mathematics Subject Classification 47D06, 30H28 (primary), 34D05, 30H50 (secondary).

The third author was partially supported by a KBN grant.


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