Question

real analysis

13 Suppose fis a continuous function on R, with period 1. Prove that lim Σ f(a)-| f(t) dt 0 for every irrational real number

hint

4.13 Let 2 be the set of functions of form P(t)-Σ_NQC2nikt. The equality holds for functions in . For given ε > 0, there is a

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od 1 at f(t): eep (QTTİ kt).stf1寸2, exp(2riko N rN Hem Ce floa)at d0 be the getaS.functionsof叶ae.fama af e>o “nen, 3 ped suda taak.fll-PuSa a.4 시K e. nl

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