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Uncertainty principles and signal recovery. (English) Zbl 0689.42001

Summary: The uncertainty principle can easily be generalized to cases where the “sets of concentration” are not intervals. Such generalizations are presented for continuous and discrete-time functions, and for several measures of “concentration” (e.g., \(L_ 2\) and \(L_ 1\) measures). The generalizations explain interesting phenomena in signal recovery problems where there is an interplay of missing data, sparsity, and bandlimiting.

MSC:

42A05 Trigonometric polynomials, inequalities, extremal problems
94A11 Application of orthogonal and other special functions
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