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The Lebesgue Constants for (γ, r) Summation of Fourier Series
Published online by Cambridge University Press: 20 November 2018
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The (γ, r) summation method, 0 < r < 1, is the "circle method" employed by G. H. Hardy and J. E. Littlewood. It is also known as the Taylor method. Its Lebesgue constants, say L(Tr, n), n = 1, 2, …, were studied by K. Ishiguro [1] in the notation L*(n;1-r). He noted that
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where Im{z} denotes the imaginary part of the complex number z, and proved that
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Here
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- Copyright © Canadian Mathematical Society 1963
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