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Cesaro Summation of the Differentiated Series of Fourier‐Lebesgue Series and their Allied Series
Author(s) -
Sayers K. I.
Publication year - 1930
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s2-31.1.29
Subject(s) - series (stratigraphy) , mathematics , fourier series , lebesgue integration , bounded variation , conjugate fourier series , mathematical analysis , alternating series , pure mathematics , fourier transform , fourier analysis , power series , paleontology , short time fourier transform , biology
In this paper I discuss the summability of the differentiated series of Fourier‐Lebesgue series and their allied series on lines similar to those adopted by Plessner‡, but remove the restriction that F ( x ) is to be a function of bounded variation. The general case of summability ( C, k ) for k > 0 for the differentiated series and k > 1 for the allied series is discussed, and known results are deduced as apecial cases.