40 citations · 207 across the 29 of their papers we have counts for
8 papers · 1 filter
Uniform convergence of Fourier-Bessel series on a q-linear grid
L. D. Abreu, R. Álvarez-Nodarse, J. L. Cardoso
We study Fourier-Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficien…
Sharp rates of convergence for accumulated spectrograms
Luís Daniel Abreu, João Pereira, José Luis Romero
We investigate an inverse problem in time-frequency localization: the approximation of the symbol of a time-frequency localization operator from partial spectral information by the…
The bias-variance trade-off in Thomson's multitaper estimator
Luís Daniel Abreu, José Luis Romero
At the heart of non-parametric spectral estimation, lies the dilemma known as the bias-variance trade-off: low biased estimators tend to have high variance and low variance estimat…
On accumulated spectrograms
Luís Daniel Abreu, Karlheinz Gröchenig, José Luis Romero
We study the eigenvalues and eigenfunctions of the time-frequency localization operator on a domain of the time-frequency plane. The eigenfunctions are the appropriate pr…
Wavelet frames, Bergman spaces and Fourier transforms of Laguerre functions
Luis Daniel Abreu
The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets…
Hardy-type theorem for functions orthogonal with respect to their zeros. The Jacobi weight case
L. D. Abreu, F. Marcellan, S. Yakubovich
Motivated by G. H. Hardy's 1939 results \cite{Hardy} on functions orthogonal with respect to their real zeros , we will consider, within the same general conditi…