Uniform limit power-type function spaces

In literature of Fourier transforms and Wavelet transforms, the basic space is L2(R). From the point of view of signal analysis, a signal f ∈ L2(R) can only be transient (or “wavelets”). During recent years in some application areas, it has become more common to motivate a theory via persistent rather than transient signals (e.g., [16, 28, 30, 42]). To work on persistent signals, people have to seek a space different from L2(R). One important example of such spaces is (R), the space of almost periodic functions. People have developed a profound theory and applications for (R) (e.g., see [4, 5, 7– 15, 18, 19, 24, 26, 30, 32, 37, 38]). As in [30], a function f is called limit power if the limit