Revista Matemática Iberoamericana


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Volume 28, Issue 1, 2012, pp. 93–112
DOI: 10.4171/RMI/668

Published online: 2012-01-20

Boundary uniqueness of harmonic functions and spectral subspaces of operator groups

Alexander Borichev[1] and Yuri Tomilov[2]

(1) Aix Marseille Université, Marseille, France
(2) Nicolaus Copernicus University, Toruń, Poland

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on Banach spaces.

Keywords: Uniqueness theorems, harmonic functions, approach regions, spectral subspaces, operator groups

Borichev Alexander, Tomilov Yuri: Boundary uniqueness of harmonic functions and spectral subspaces of operator groups. Rev. Mat. Iberoamericana 28 (2012), 93-112. doi: 10.4171/RMI/668