Suppose that (on) is an approximate identity on T and =1 fe L (T). (a) Prove...

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Suppose that (on) is an approximate identity on T and =1 fe L¹ (T). (a) Prove that for every n EN (b) Prove that ||₁ *f|₁ ≤||f||₁. ||øn* f- f₁ → 0 (c) If f. g € L¹(T) have the same Fourier coefficients, prove that f = g. as n → ∞. Suppose that (on) is an approximate identity on T and =1 fe L¹ (T). (a) Prove that for every n EN (b) Prove that ||₁ *f|₁ ≤||f||₁. ||øn* f- f₁ → 0 (c) If f. g € L¹(T) have the same Fourier coefficients, prove that f = g. as n → ∞.

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