On Bases in the Space of Vector Valued Entire Dirichlet Series of Two Complex Variables
نویسندگان
چکیده
The space of all entire functions represented by vector valued Dirichlet series of two complex variables is considered in this paper. It is equipped with two equivalent topologies. The main result of this paper is concerned with finding the conditions for a base in Xto become a proper base and certain continuous linear operators which are used to determine the proper bases inX.
منابع مشابه
Relative order and type of entire functions represented by Banach valued Dirichlet series in two variables
In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...
متن کاملGeneralized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series
In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.
متن کاملSome study on the growth properties of entire functions represented by vector valued Dirichlet series in the light of relative Ritt orders
For entire functions, the notions of their growth indicators such as Ritt order are classical in complex analysis. But the concepts of relative Ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. Therefore the studies of the growths of entire functions in the light of thei...
متن کاملOn Some Results in the Light of Generalized Relative Ritt Order of Entire Functions Represented by Vector Valued Dirichlet Series
In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.
متن کاملSpaces of entire functions represented by vector valued Dirichlet series of slow growth
Spaces of all entire functions f represented by vector valued Dirichlet series and having slow growth have been considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous transformations is characterized. Proper bases have also been characterized in terms of growth parameters.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012