7. [6 points) A T-periodic function h: R + R is called piecewise continuous if there exists decomposition 0 = to

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7 6 Points A T Periodic Function H R R Is Called Piecewise Continuous If There Exists Decomposition 0 To Ti 1 (22.31 KiB) Viewed 29 times

7. [6 points) A T-periodic function h: R + R is called piecewise continuous if there exists decomposition 0 = to <tı <... <tm = T of the interval [0, T) such that h(t) is continuous on (tx-1, tk), k = 1,...,m and there exist one-sided limits of h(t) at tk. Let f.9: R+R be two piecewise continuous T-periodic functions with identical Fourier coefficients. Show that f(t) = g(t) for all t € R except those t where f and g have jumps.