Decide if the statements below are true or false.
By "different" we mean, there exists at least one in the domain of and such that .

Question

Decide if the statements below are true or false. 
 By "different" we mean, there exists at least one    in the domain of    and    such that   .

Answer

The Fourier series of a function    always converges pointwise to   .

Answer

The Fourier series of a trigonometric polynomial    always converges pointwise to   .

Answer

Two different discontinuous functions    might share the same Fourier coefficients.

Answer

Fourier series do not converge uniformly near discontinuities.

Answer

The Fourier series of a function    always converges uniformly to   .

Answer

Fourier partial sums are continuous functions.

Answer

Two different continuous functions    might share the same Fourier coefficients.

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