6. [SUMMABILITY KERNELS]. Let N : R ----; R be a sequence of continuous, periodic functions on...
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6. [SUMMABILITY KERNELS]. Let ¢N : R ----; R be a sequence of continuous, periodic functions on R that satisfy r27r io ¢N(t) dt = 1 and for all N E N, and for each 0 < 8 < 2n. Suppose that f: R ----; R is continuous and periodic.
Prove that 127r lim f(x - t)¢N(t) dt = f(x)
N~oo 0 uniformly for x E R.
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