Time Frequency Representations of Almost Periodic Functions |
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| Authors: | Yeon Hyang Kim Amos Ron |
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| Affiliation: | (1) Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, WI 53706, USA;(2) Computer Sciences Department, University of Wisconsin-Madison, 1210 West Dayton, Madison, WI 53706, USA |
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| Abstract: | 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 L 2(ℝ)-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 L 2(ℝ) representations and AP-representations. |
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| Keywords: | Frames Time frequency representations Almost-periodic functions Weyl– Heisenberg systems Affine systems Dual Gramian Fiberization of time frequency representations AP-frames |
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