On L1-Convergence of Fourier Series under the MVBV Condition
2009 ◽
Vol 52
(4)
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pp. 627-636
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Keyword(s):
AbstractLet f ∈ L2π be a real-valued even function with its Fourier series , and let Sn( f , x), n ≥ 1, be the n-th partial sum of the Fourier series. It is well known that if the nonnegative sequence ﹛an﹜ is decreasing and limn→∞an = 0, thenWe weaken the monotone condition in this classical result to the so-called mean value bounded variation (MVBV) condition. The generalization of the above classical result in real-valued function space is presented as a special case of the main result in this paper, which gives the L1-convergence of a function f ∈ L2π in complex space. We also give results on L1-approximation of a function f ∈ L2π under the MVBV condition.
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1990 ◽
Vol 33
(2)
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pp. 169-180
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1966 ◽
Vol 62
(4)
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pp. 637-642
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1973 ◽
Vol 5
(02)
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pp. 217-241
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1950 ◽
Vol 46
(1)
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pp. 111-115
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2014 ◽
Vol 14
(2)
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pp. 117-122
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1992 ◽
Vol 34
(1)
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pp. 1-9
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1968 ◽
Vol 64
(1)
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pp. 61-66
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