Abstract This article considers the weighted space of entire functions of multiple complex variables, which is defined as the projective limit of Banach spaces. Necessary conditions on the weight functions that ensure the invariance of the space under differentiation and translation are presented. Theorem 3 proves the hypercyclicity in this space of an operator, which is a finite sum of combinations of multiplication by a variable and a differential operator. In Theorem 5, the chaotic and frequently hypercyclic properties of the this operator in this considered space are given. Theorem 4 shows the hypercyclicity of the composition operator of differentiation and shift. In Theorem 6, its chaoticity and frequently hypercyclicity in this space are proved.
A. I. Rakhimova (Sun,) studied this question.
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