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Published online by Cambridge University Press: 20 November 2018
Sumner (3) discussed for arbitrary real λ and h, where the averaging operator ∇h is defined by
(1.1)
when f(z) is an entire function of exponential type <2π/|h|. Boas (2) gave an alternative definition of ∇h which gave Sumner's results quickly and showed that his definition is equivalent to that of Sumner.