Time frequency representations of almost-periodic functions
نویسندگان
چکیده
In this paper, we characterize the space of almost periodic (AP ) functions in one variable using either a Weyl-Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively, affine) system is an L2(IR)-frame. Moreover, the frame bounds of the system are also the sharpest bounds in our characterization. This draws an intriguing and quite unexpected connection between L2(IR) representations and AP representations. AMS (MOS) Subject Classifications: Primary 42C40, Secondary 42A75
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