Trigonometric series with a generalized monotonicity condition
نویسندگان
چکیده
Abstract In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.
منابع مشابه
The Ultimate Condition to Generalize Monotonicity for Uniform Convergence of Trigonometric Series
Chaundy and Jolliffe [1] proved that if {an} is a non-increasing (monotonic) real sequence with lim n→∞ an = 0, then a necessary and sufficient condition for the uniform convergence of the series P∞ n=1 an sinnx is lim n→∞ nan = 0. We generalize (or weaken) the monotonic condition in this well-known result to the so-called mean value bounded variation condition and prove that the generalized co...
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