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On Frame Properties of Iterates of a Multiplication Operator

  • Zaur A. Kasumov
  • Aydin Sh. ShukurovEmail author
Article
  • 34 Downloads

Abstract

Dynamical sampling that is a relatively new research topic in applied harmonic analysis has attracted considerable attention in recent years. One of the central problems in dynamical sampling is investigation of frame properties for families of elements obtained by iterates of operators. Note that investigation of basicity properties of iterates of operators is problematic even in the case of well known “standard” operators. In this note we consider iterates of the multiplication operator \(T_\varphi x(t)=\varphi (t)x(t), x \in L_2(a,b)\) and show that it cannot form a frame for the space \(L_2(a,b)\).

Keywords

Dynamical sampling operator orbit frame Schauder bases system of powers Lebesgue spaces 

Mathematics Subject Classification

42C15 46E30 46B25 46B15 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsNAS of AzerbaijanBakuAzerbaijan
  2. 2.Department of MathematicsKhazar UniversityBakuAzerbaijan

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