ON SOME APPLICATIONS OF DUHAMEL OPERATORS

Tapdigoglu R., Altwaijry N.

MATHEMATICA SLOVACA, vol.72, no.5, pp.1375-1381, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1515/ms-2022-0093
  • Journal Name: MATHEMATICA SLOVACA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.1375-1381
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

Let D = {z is an element of C : vertical bar z vertical bar < 1} be the unit disk and Hol(D x D) be the space of all holomorphic functions on the bi-disc D x D. We consider the double convolution operator K-f on the subspace Hol(zw)(D x D) := {f is an element of Hol(D x D) : f(z, w) = g(zw) for some g is an element of Hol(D)} defined by (K(f)h) (zw) = (f * h) (zw) := integral(z)(0) integral(w)(0) f((z - u) (w - v))h(uv) dvuv. We study extended eigenvalues of K-f. We characterize extended eigenvectors of K-f in terms of Duhamel operators. Moreover, we describe cyclic vectors of operator K-f by applying the Duhamel product method. (C) 2022 Mathematical Institute Slovak Academy of Sciences