Let be a Banach space of complex valued functions that are continuous on the closed bidisc , where is the unit disc in the complex plane and has th partial derivatives in which can be extended to functions continuous on . The Duhamel product is defined on by the formula In the present paper we prove that is a Banach algebra with respect to the Duhamel product . This result extends some known results. We also investigate the structure of the set of all extended eigenvalues and extended eigenvectors of some double integration operator . In particular, the commutant of the double integration operator is also described.
"On the Banach algebra structure for of the bidisc and related topics." Illinois J. Math. 64 (2) 185 - 197, June 2020. https://doi.org/10.1215/00192082-8303477