M. Riesz-Schur-type inequalities for entire functions of exponential type
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© 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. We prove a general M. Riesz-Schur-type inequality for entire functions of exponential type. If f and Q are two functions of exponential types σ > 0 and τ ≥ 0, respectively, and if Q is real-valued and the real zeros of Q, not counting multiplicities, are bounded away from each other, then (Equation presented) We apply this inequality to the weights Q(x)def = sin(τx) and Q(x)def= x and describe the extremal functions in the corresponding inequalities.
author list (cited authors)
Ganzburg, M. I., Nevai, P., & Erdélyi, T.