4. Suppose that f : R --+ R is periodic, piecewise continuous, and of bounded variation on...
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4. Suppose that f : R --+ R is periodic, piecewise continuous, and of bounded variation on R. Prove that if S is a trigonometric series that converges to
(f(x+) + f(x-) )/2 for all x E R, then S is the Fourier series of f.
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