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I have seen a result on termwise differentiation of Fourier series:

If$ f $ is periodic with period $ 2l $, continuous on $ \mathbb{R} $ and $ f' $ is piecewise continuous on $ [−l,l] $, then the Fourier Series of $ f $ can be differentiated termwise.

Above result is migirated from Doubt Regarding Termwise differentiation of Fourier Series . It is really useful to my current research. Could anyone help with reference on above result?

Thanks in advance!

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The result in this question could be found in

Kenneth B. Howell: Principles of Fourier Analysis, Chapman & Hall/CRC, Boca Raton, Fla, 2001.

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