Boundary uniqueness of harmonic functions and spectral subspaces of operator groups

2010/03/14 by Alexander Borichev, Yuri Tomilov, Borichev, Alexander +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 31A20 #Secondary 47D06 #math.CV #math.FA #msc:31A20 #msc:47D06

paper · pdf · doi:10.48550/arxiv.1003.2805

21 pages

arxiv created 2010/03/14 · arxiv updated 2010/03/16

Abstract

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.

Related

• Uniqueness theorems for (sub-)harmonic functions with applications to operator theory
• Uniqueness theorem for unbounded domain
• Topics in Hilbert Spaces, Spectral Theory, and Harmonic Analysis
• The Dirichlet problem and spectral theory of operator algebras
• Uniqueness theorems for subharmonic functions