It is not the purpose of this paper to construct approximations but to establish a class of almost periodic functions which can be approximated, with an arbitrarily prescribed accuracy, by continuous periodic functions uniformly on .
The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid....
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