scholarly journals On the Integral Modulus of Continuity of Fourier Series

1988 ◽  
Vol 44 (2) ◽  
pp. 151-158
Author(s):  
Babu Ram ◽  
Suresh Kumari
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Modulus Of Continuity ◽  
Wide Class ◽  
Integral Modulus

AbstractFor a wide class of sine trigonometric series we obtain an estimate for the integral modulus of continuity.

scholarly journals Fourier series with small gaps

1989 ◽  
Vol 46 (2) ◽  
pp. 212-219
Author(s):  
P. Isaza ◽  
D. Waterman
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Order Condition ◽  
Circle Group ◽  
The Difference ◽  
Bounded Below

AbstractA trigonometric series has “small gaps” if the difference of the orders of successive terms is bounded below by a number exceeding one. Wiener, Ingham and others have shown that if a function represented by such a series exhibits a certain behavior on a large enough subinterval I, this will have consequences for the behavior of the function on the whole circle group. Here we show that the assumption that f is in any one of various classes of functions of generalized bounded variation on I implies that the appropriate order condition holds for the magnitude of the Fourier coefficients. A generalized bounded variation condition coupled with a Zygmundtype condition on the modulus of continuity of the restriction of the function to I implies absolute convergence of the Fourier series.

scholarly journals On trigonometric approximation of functions in the Lq norm

2018 ◽  
Vol 51 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Ram N. Mohapatra ◽  
Bogdan Szal
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Infinite Matrix ◽  
Approximation Of Functions ◽  
Integral Modulus

Abstract In this paper we obtain a degree of approximation of functions in Lq by operators associated with their Fourier series using integral modulus of continuity. These results generalize many known results and are proved under less stringent conditions on the infinite matrix.

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