| The paper consists of two parts : one part concerns on the generalizations of Besicovitch almost periodic functions to the case of functions of more than one parameter, the other part concerns on the applications of uniformly Besicovitch almost periodic functions to differential equations.On the generalizations of Besicovitch almost periodic functions, the main works are as follows:To begin with, based on different notions of the distance of two functions in the space of CLP(D × R, Cn), the theories of Stepanoff, Weyl and Besicovitch almost periodic functions can be generalized respectively to the space of CLP{D × R, Cn). For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.On the applications of the uniformly Besicovitch almost periodic functions to differential equations, the main works are as follows:First, the paper proves that the space of the uniformly B2 almost periodic functions, with a special norm, is a Banach space, and then the Fixed Point Methods could be used in this function space.Second, since the space of the uniformly B2 almost periodic functions is per-fect, the paper investigates the existence and uniqueness of uniformly B2 almost periodic solution of a wave equation involving reflection of the argument by the principle of contraction mapping.
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