scholarly journals On the |K λ|-summability of Fourier series and its conjugate series

2015 ◽  
Vol 5 (1) ◽  
pp. 35-50
Author(s):  
Sanghamitra Beuria ◽  
G. Das ◽  
B. K. Ray
Keyword(s):  
Fourier Series ◽  
Conjugate Series ◽  
Summability Of Fourier Series

Approximation of Signals by Harmonic-Euler Triple Product Means

2021 ◽  
Vol 88 (1-2) ◽  
pp. 176
Author(s):  
Smita Sonker ◽  
Paramjeet Sangwan
Keyword(s):  
Fourier Series ◽  
Triple Product ◽  
Conjugate Series ◽  
Summability Of Fourier Series ◽  
Approximation Of Signals ◽  
General Conditions

Our paper deals with the approximation of signals by <em>H<sub>1</sub>.E<sup>θ</sup>.E<sup>θ</sup></em> product means of Fourier and its conjugate series. New theorems based on <em>H<sub>1</sub>.E<sup>θ</sup>.E<sup>θ</sup></em> product summability have been established and proved under general conditions. The established theorems extend, generalize and improve various existing results on summability of Fourier series and its conjugate series.

A New Criterion for Borel Summability of Fourier Series

1969 ◽  
Vol 12 (5) ◽  
pp. 573-580 ◽  
Author(s):  
B.N. Sahney ◽  
P.D. Kathal
Keyword(s):  
Fourier Series ◽  
Sufficient Conditions ◽  
Borel Summability ◽  
Conjugate Series ◽  
Summability Of Fourier Series ◽  
New Criterion

The application of Borel summability to Fourier series has been discussed by Takahashi and Wang [8] and Sahney [5]. Sahney [6] and Sinvhal [7] obtained sufficient conditions for the Borel summability of the derived Fourier series and its conjugate series, respectively. Kathal [3] obtained different conditions in the case of the conjugate series. In this paper we give a new criterion for Borel summability of Fourier series.

scholarly journals Absolute Riesz summability of Fourier series and their conjugate series

1970 ◽  
Vol 3 (2) ◽  
pp. 217-229
Author(s):  
Masako Izumi ◽  
Shin-ichi Izumi
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Conjugate Series ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Summability Of Fourier Series ◽  
Series Of Functions

This paper contains two theorems. The first theorem treats the |R, r, l| summability of Fourier series and their associated series of functions of bounded variation. The second concerns the |R, r, l| summability of Fourier series of functions f such that φ(t)m(l/t) is of bounded variation where m(u) increases to infinity as u → ∞. These theorems generalize Mohanty's theorems.

scholarly journals ON $(N , p_n, q_n)$ SUMMABILITY OF FOURIER SERIES AND ITS CONJUGATE SERIES

1994 ◽  
Vol 25 (2) ◽  
pp. 93-99
Author(s):  
NARENDRA KUMAR SHARMA ◽  
RAJIV SINHA
Keyword(s):  
Fourier Series ◽  
Conjugate Series ◽  
Summability Of Fourier Series

The aim of the present paper is to generalize the result of the theorems given by Pandey [4].

scholarly journals On the study of conjugate series of a Fourier series by $ K^\lambda$-summability methods

2003 ◽  
Vol 34 (2) ◽  
pp. 147-154
Author(s):  
Shyam Lal ◽  
Prem Narain Singh
Keyword(s):  
Fourier Series ◽  
Conjugate Series ◽  
Summability Methods ◽  
Summability Of Fourier Series

Vukovic (1965) and Kathal (1969) have studied the $ K^\lambda$-summability of Fourier series. In this paper, generalizing an earlier result of Kathal, a theorem on $ K^\lambda$-summability of conjugate series of a Fourier series has been established.

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