The Ultimate Condition to Generalize Monotonicity for Uniform Convergence of Trigonometric Series
نویسندگان
چکیده
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 condition cannot be weakened further. We also establish an analogue to the generalized Chaundy and Jolliffe theorem in the complex space.
منابع مشابه
Trigonometric series with a generalized monotonicity condition
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