A function f is said to be an almost periodic polynomial if it can be expressed in the form formula (cell) The set of all almost periodic polynomials forms an algebra APp. The closure of APp under the uniform norm ‖f‖ = sup_x∈R|f(x)| gives the algebra AP of almost Periodic functions. In other words, AP is the C~*-subalgebra of L~∞(R) generated By all functions eλ(x) = e~iλx, λ∈R. The mean value of an almost periodic function is defined as A Formula (ell.).......... And the Fourier coefficient M_λ(f): = M(e_λf).
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