Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary

Abanin, A. V. , Varziev V. A.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 4.

Abstract:
We consider \((LB)\) spaces of functions which are holomorphic in a convex domain and have a finite type with respect to an order near its boundary. Using Laplace
transformation, we give a description of their duals. Then we characterize mimimal absolutely representing systems of exponential functions in these spaces and prove that they always exist.

Keywords: spaces of holomorphic functions with a given growth, absolutely representing systems, systems of exponential functions

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