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Uncertainty principles as embeddings of modulation spaces |
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| Authors: | Yevgeniy V Galperin |
| Institution: | a Department of Mathematics, Sacred Heart University, Fairfield, CT, USA b Department of Mathematics U-3009, University of Connecticut, Storrs, CT 06269-3009, USA |
| Abstract: | A class of new uncertainty principles is derived in the form of embeddings of Fourier-Lebesgue spaces into modulation spaces. These embeddings provide practical, sufficient conditions for a function to belong to a modulation space. Counterexamples based on the properties of Gabor expansions demonstrate that the embeddings are optimal. |
| Keywords: | Uncertainty principle Modulation space Short-time Fourier transform Gabor expansion Embedding of function spaces |
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