On the Absolute Cesaro Summability of Negative Order for a Fourier Series at a Given Point

1944 ◽  
Vol 66 (2) ◽  
pp. 299 ◽  
Author(s):  
Kien-Kwong Chen
Keyword(s):  
Fourier Series ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Negative Order ◽  
The Absolute

On the Absolute Cesaro Summability of Negative Order of a Series Associated with the Conjugate Series of a Fourier Series

1969 ◽  
Vol 21 ◽  
pp. 552-557
Author(s):  
R. Mohanty ◽  
B. K. Ray
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Cesàro Summability ◽  
Conjugate Series ◽  
Cesaro Summability ◽  
Period 2 ◽  
Negative Order ◽  
Fixed Positive Number ◽  
The Absolute ◽  
Image Position

1. Definition. Let λ ≡ λ(ω) be continuous, differentiable, and monotonie increasing in (0, ∞) and let it tend to infinity as ω → ∞. A series an is summable |R, λ, r|, where r > 0, ifwhere A is a fixed positive number (6, Definition B).Let f(t) be a periodic function with period 2π and Lebesgue integrable over (–π, π) and let1.1The series conjugate to (1.1), at t = x, is1.2

scholarly journals A criterion for absolute Cesàro summability of negative order of a Fourier series

1965 ◽  
Vol 14 (4) ◽  
pp. 311-319
Author(s):  
Yung-Ming Chen
Keyword(s):  
Fourier Series ◽  
Arbitrary Constant ◽  
Conjugate Function ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Negative Order

Let f(x) be integrable L(0, 2π) and periodic with period 2π, and let ψ(t) be the conjugate function of with respect to the variable t, where x is onsidered as an arbitrary constant. The following theorems are due to K. K. Chen (1), (2), pp. 111–124.

scholarly journals The Absolute Cesaro Summability of the Successively Derived Allied Series of a Fourier Series

1950 ◽  
Vol 8 (4) ◽  
pp. 163-176
Author(s):  
R. Mohanty
Keyword(s):  
Fourier Series ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
The Absolute ◽  
Image Position

We suppose that f(t) is integrable in the Lebesgue sense m (π, π) and is periodic with period 2π. We denote its Fourier series byThen the allied series is

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