Question: 1.29. Define for each n: f (n = [ e27rinx u(dx ~t( ) Jw ') Prove by WeIerstrass ' s approxImatIOn theorem (by tngonometncal

1.29. Define for each n:

f (n \ = [ e27rinx u(dx\ ~t( ) Jw ""')

Prove by WeIerstrass ' s approxImatIOn theorem (by tngonometncal polyno mials) that if 11*, (n) = 11*2 (n) for every n > 1 , then J.-L 1 = U2. The conclusion becomes false if 11 is replaced by [0, 1].

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