Speaker
Description
We give a scale of completeness conditions for exponential systems in spaces of continuous functions on a compact set of the complex plane that are simultaneously holomorphic inside a compact set, in spaces of holomorphic functions in a domain, and so on. These conditions will be formulated in geometric terms of mixed areas for the convex hull of a compact or domain. We will characterize the distribution of exponents of the exponential system both in terms of their modules and in terms of arguments using various options for the convexity of functions. The vast majority of known results on the completeness of exponential systems in such spaces turn out to be very special cases from this scale. Our completeness results extend to parameterized systems of entire functions, which are more general than exponential systems. All studies cover several complex variables.
