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Keywords:

  • Appell sequences;
  • umbral calculus;
  • MSC (2010);
  • 47B37;
  • 46A45;
  • 05A40

Abstract

In the context of Köthe spaces we study the bases related with the backward unilateral weighted shift operator, the so-called generalized derivation operator, extending known results for spaces of analytic functions. These bases are a subclass of Sheffer sequences called generalized Appell sequences and they are closely connected with the isomorphisms invariant by the weighted shift. We use methods of the non classical umbral calculi to give conditions for a generalized Appell sequence to be a basis.