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https://doi.org/10.1007/s10444-004-4145-x
Title: | Inequalities on time-concentrated or frequency-concentrated functions | Authors: | Goh, S.S. Goodman, T.N.T. |
Keywords: | Extremal functions Measures of spread Time- or frequency-concentrated functions Uncertainty principles |
Issue Date: | Jan-2006 | Citation: | Goh, S.S., Goodman, T.N.T. (2006-01). Inequalities on time-concentrated or frequency-concentrated functions. Advances in Computational Mathematics 24 (1-4) : 333-351. ScholarBank@NUS Repository. https://doi.org/10.1007/s10444-004-4145-x | Abstract: | We obtain an inequality on a measure of the spread in time of periodic functions that are ε-concentrated in frequency, i.e. all but a fixed finite number of Fourier coefficients vanish with mean-squared error up to ε. We characterize an extremal function and give an asymptotic formula for the measure of spread of this extremal function as ε approaches 0. We also consider the corresponding problem for functions on the real line that are ε-concentrated in time or frequency. When ε=0, the above reduce to inequalities on time-limited or band-limited functions and these are discussed in more detail. © Springer 2006. | Source Title: | Advances in Computational Mathematics | URI: | http://scholarbank.nus.edu.sg/handle/10635/103417 | ISSN: | 10197168 | DOI: | 10.1007/s10444-004-4145-x |
Appears in Collections: | Staff Publications |
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