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It the following correct?

If the series of the Fourier coefficients is absolute convergent then the Fourier series is uniform convergent.

Is it related to some theorem? Parseval's identity?

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If the series of Fourier coefficients are absolute convergent, then the series of functions $$\sum_{n=-\infty}^\infty (t\mapsto\hat{f}(n)e^{int})$$ is uniform convergent by Weierstrass M-test, since: $$\sum_{n=-\infty}^\infty \|t\mapsto\hat{f}(n)e^{int}\|_\infty=\sum_{n=-\infty}^\infty |\hat{f}(n)|<+\infty$$

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