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math.FA2017
A planar large sieve and sparsity of time-frequency representations
Luis Daniel Abreu, Michael Speckbacher
With the aim of measuring the sparsity of a real signal, Donoho and Logan introduced the concept of maximum Nyquist density, and used it to extend Bombieri's principle of the large…
math.FA2015★ 2 cited
Pseudo prolate spheroidal functions
Luís Daniel Abreu, João M. Pereira
Let and denote the operators which cut the time content outside and the frequency content outside , respectively. The prolate spheroidal functions are the ei…
math.FA2014★ 18 cited
Measures of localization and quantitative Nyquist densities
Luís Daniel Abreu, João M. Pereira
We obtain a refinement of the degrees of freedom estimate of Landau and Pollak. More precisely, we estimate, in terms of , the increase in the degrees of freedom resulting upon…