2 research outputs found
On an entire function represented by multiple Dirichlet series
summary:Consider the space of entire functions represented by multiple Dirichlet series that becomes a non uniformly convex Banach space which is also proved to be dense, countable and separable. Continuing further, for the given space the characterization of bounded linear transformations in terms of matrix and characterization of linear functional has been obtained
On a class of vector-valued entire Dirichlet series in n variables
We consider a class F of entire Dirichlet series in n variables, whose coefficients belong to a commutative Banach algebra E. With a well defined norm, F is proved to be a Banach algebra with identity. Further results on quasi-invertibility, spectrum and continuous linear functionals are proved for elements belonging to F