On some applications of Duhamel product

Karaev M. T. , Tuna H.

LINEAR & MULTILINEAR ALGEBRA, vol.54, no.4, pp.301-311, 2006 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2006
  • Doi Number: 10.1080/03081080512331318481
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.301-311


Let C-A((n))(D) denote the algebra of all n-times continuously differentiable functions on (D) over bar which are holomorphic on the unit disc D = {z is an element of C: \z\< 1}. We prove that C-A((n))(D) is a Banach algebra with multiplication as Duhamel product (f*g)(z) = d/dz integral(z)(o) f(z - )g(t)dt and describe its maximal ideal space. We also describe the commutant and strong cyclic vectors of the integration operator (Tf)(z) = integral(z)(o)f(t)dt. Using the Duhamel product we also study the extended eigenvalues and the corresponding extended eigenvectors of the integration operator T.