The integral modulus of continuity of functions with quasiconvex fourier coefficients

1971 ◽  
Vol 11 (5) ◽  
pp. 847-851 ◽  
Author(s):  
S. A. Telyakovskii
Keyword(s):  
Modulus Of Continuity ◽  
Fourier Coefficients ◽  
Integral Modulus

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 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.

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