Please use this identifier to cite or link to this item: 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
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