= Kahane-Katznelson divergence theorem
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= Kahane and Katznelson theorem
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Every null subset of the circle lies in the divergence set of the <Fourier series> of some continuous complex-valued <function>. One can arrange unbounded <Fourier partial sums> there. The <compact-set Fourier amplification lemma>, <compact batching of a small open set> and <frequency-separated Fourier block series> construct the function by a summable series of small blocks. The result covers nonclosed and dense null sets; it does not require the divergence set to equal the originally specified set.
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