DUHAMEL BANACH ALGEBRA STRUCTURE OF SOME SPACE AND RELATED TOPICS

Altintas M., Guerdal M., Tapdigoglu R.

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, vol.112, no.126, pp.83-93, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 112 Issue: 126
  • Publication Date: 2022
  • Doi Number: 10.2298/pim2226083a
  • Journal Name: PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Central & Eastern European Academic Source (CEEAS), MathSciNet, zbMATH
  • Page Numbers: pp.83-93
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

Let alpha be a fixed complex number, and let Omega be a simply connected region in complex plane C that is starlike with respect to alpha is an element of Omega. We define some Banach space of analytic functions on Omega and prove that it is a Banach algebra with respect to the alpha-Duhamel product defined by (f circle star alpha g) (z) : = d/dz integral(z)(alpha)f(z + alpha - t)g(t) dt. We prove that its maximal ideal space consists of the homomorphism h(alpha) de-fined by h(alpha) (f) = f (alpha). Further, we characterize the lattice of invariant sub-spaces of the integration operator J(alpha) f (z) = f(alpha)(z)f (t) dt. Moreover, we describe in terms of alpha-Duhamel operators the extended eigenvectors of J(alpha).