We study the structure of generators of the Banach algebras ( W (n) p [0,1], ∗ α ) and ( W (n) p [0,1],⊛ ) , where ∗ α denotes the convolution product ∗ α defined by ( f ∗ α g ) (x) := R x 0 f (x+α −t)g(t)dt, and the so-called Duhamel product ⊛. We also give some description of cyclic vectors of usual convolution operators acting in the Sobolev space W (n) p [0,1] by the formula Kk f (x) = R x 0 k (x−t) f (t)dy.
Digital Object Identifier (DOI)
Gurdal, Mehmet; Saltan, Suna; and Yamancı, Ulaş
"Generators of Certain Function Banach Algebras and Related Questions,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 61.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss1/61