Abstract:
We study whether an entire function of exponential type has totally regular growth if its derivative increases sufficiently fast on the zero set of the function itself. In particular, for a function with a trigonometrically convex (or positive) lower indicator, we obtain a solution of a well-known problem of Leont'ev. As an application, we refine some already known results concerning the characterization of exponents of the representing systems of exponentials.
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