The convolution of two differentiable functions on the circle need not be differentiable
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The convolution operator is well-known for preserving the best properties of its parent functions, and is often presented as a “smoothing” operator. In the present result, we construct two differentiable functions whose convolution is not differentiable.
KeywordsConvolution Non differentiable function Lineability Spaceability Algebrability
Mathematics Subject Classification44A35 58B10 54C30
The authors would like to thank prof. Fedor Nazarov for his kind and selfless help in outlining the ideas that crystallized in the counter examples that resulted in Theorem 2.1.