scholarly journals Generalized Cesaro Summability of Fourier Series and Its Applications

2021 ◽  
Author(s):  
Oktay DUMAN
Keyword(s):  
Fourier Series ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Summability Of Fourier Series

On the Cesàro summability of Fourier series and Allied series

1930 ◽  
Vol 26 (2) ◽  
pp. 173-203 ◽  
Author(s):  
R. E. A. C. Paley
Keyword(s):  
Fourier Series ◽  
Cesàro Summability ◽  
Cesàro Mean ◽  
Cesaro Summability ◽  
Cesaro Mean ◽  
Summability Of Fourier Series ◽  
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For r>-1, let denoteIfwe say that the series a0 + a1 + a2 +…+an+… is summable by Cesàro mean of order r, or more shortly summable (C, r) to sum s. If r >−1, andwe say that the series is summable by Rieszian mean of order r to the sum s. It has been shown that these two methods of summation are equivalent. Throughout this paper I shall deal with the Rieszian mean, but I shall retain the symbol (C, r). It is known† that if a series is summable (C, r), it is also summable (C, r′) to the same sum for all numbers r′ greater than r.

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