We consider the space X of all analytic functionsf(s1 ,s2) = ∞∑aminexp(s1λm+s2μtn)of two complex variables s1 and s2, equipping it with the natural locally convex topology and using thegrowth parmeter, the order of f as defined recently by the authors. Under this topology X becomes aFrechet space. Apart from finding the characterization of continuous linear functiors, linear transforma-tion on X, we have obtained the necesary and sufficient conditions for a double sequence in X to be a properbases.
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