The Lebesgue Constants for (γ, r) Summation of Fourier Series
Canadian mathematical bulletin, Tome 6 (1963) no. 2, pp. 179-182
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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 1 where Im{z} denotes the imaginary part of the complex number z, and proved that 2 Here 3
Lorch, Lee; Newman, Donald J. The Lebesgue Constants for (γ, r) Summation of Fourier Series. Canadian mathematical bulletin, Tome 6 (1963) no. 2, pp. 179-182. doi: 10.4153/CMB-1963-018-8
@article{10_4153_CMB_1963_018_8,
author = {Lorch, Lee and Newman, Donald J.},
title = {The {Lebesgue} {Constants} for (\ensuremath{\gamma}, r) {Summation} of {Fourier} {Series}},
journal = {Canadian mathematical bulletin},
pages = {179--182},
year = {1963},
volume = {6},
number = {2},
doi = {10.4153/CMB-1963-018-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-018-8/}
}
TY - JOUR AU - Lorch, Lee AU - Newman, Donald J. TI - The Lebesgue Constants for (γ, r) Summation of Fourier Series JO - Canadian mathematical bulletin PY - 1963 SP - 179 EP - 182 VL - 6 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-018-8/ DO - 10.4153/CMB-1963-018-8 ID - 10_4153_CMB_1963_018_8 ER -
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