On the nonconvergence of Fourier series
Sulaxana Kumari · Proceedings of the American Mathematical Society · 1958
and (ii)' an K log n/n, for some K>0, then the series (1.1), at t=0, converges. Wang [2] has also framed examples showing that k in condition (i) of Theorem A cannot be replaced by any k'<k and condition (ii)' in Theorem B cannot be replaced by the condition an = of{ nl(log n)2}. Hsiang [1] has recently tried to bridge the gap existing between conditions (ii)' and (ii) by framing examples to prove the following theorem: THEOREM C. There exists an even function 4 (t), satisfying (i)', whose Fourier series diverges at t =0, while