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Invariant subspaces and unicellularity of operators of generalized integration in spaces of analytic functionals

  • V. A. Tkachenko
Article

Abstract

Invariant subspaces are described and the unicellularity is proved of one class of operators of generalized integration in spaces of analytic functionals. As one of the realizations it is established that every nontrivial subspace, invariant relative to the integrationF(t)dt, in the space of functions analytic in an arbitrary convex domain Ω(a∃Ω), is determined by a positive integer m and consists of all functions equal to zero at pointa together with all derivatives up to order m−1.

Keywords

Positive Integer Analytic Functional Invariant Subspace Convex Domain Generalize Integration 
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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • V. A. Tkachenko
    • 1
  1. 1.Physicotechnical Low-Temperature InstituteAcademy of Sciences Ukrainian SSRUkraine

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