be the upper density. If D < ∞ and the series (1) converges uniformly on compact subsets of the complex plane C then an = 0 for all n, [2, 3, 1]. On the other hand, there are sequences of infinite density, in fact with the quotient in the RHS of (2) growing arbitrarily slowly, such that some series (1) with non-zero coefficients converges to zero uniformly… (More)
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