GELFOND-LEONTYEV GENERAL DIFFERETIATION OPERATORS AND BRENKE POLYNOMIALS

Abstract

Natural connection between Gelfond-Leontyev generalized derivation operators (GDO) and Brenke polynomials is established. Operator extension criterion commuting with GDO up to continuous H(G) space is derived. Domain class when characteristic function of the complex convolution operator always has zero type, is described. Hypercyclic and random nature of the generalized complex convolution has been proved.

Keywords

• gelfond-leontyev generalized derivative
• brenke polynomials
• dankle derivative
• commutation
• generalized complex convolution
• hypercyclic and chaotic operators.