A Moment Condition and Non-synthetic Diagonalizable Operators on the Space of Functions Analytic on the Unit Disk

  • S. M. SeubertEmail author
Differential Equations


Examples are given of (continuous, linear) operators on the space of functions analytic on the open unit disk in the complex plane having the monomials as eigenvectors, but which fail spectral synthesis (that is, which have closed invariant subspaces which are not the closed linear span of any collection of eigenvectors).


Invariant subspace spectral synthesis diagonal operator Borel series moment condition 

MSC2010 numbers

30B10 30B50 47B36 47B38 


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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Bowling Green State UniversityBowling GreenUSA

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