227 citations
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46 papers · 1 filter
Non-Asymptotic behaviour of the spectrum of the Sinc Kernel Operator and Related Applications
Aline Bonami, Philippe Jaming, Abderrazek Karoui
Prolate spheroidal wave functions have recently attracted a lot of attention in applied harmonic analysis, signal processing and mathematical physics. They are eigenvectors of the…
Random Discretization of the Finite Fourier Transform and Related Kernel Random Matrices
Aline Bonami, Abderrazek Karoui
This paper is centred on the spectral study of a Random Fourier matrix, that is an matrix whose entries are , with and two i…
An introduction to Dunkl theory and its analytic aspects
Jean-Philippe Anker
Dunkl theory is a far reaching generalization of Fourier analysis and special function theory related to root systems. During the sixties and seventies, it became gradually clear t…
An elementary proof of the positivity of the intertwining operator in one-dimensional trigonometric Dunkl theory
Jean-Philippe Anker
This note is devoted to the intertwining operator in the one--dimensional trigonometric Dunkl setting. We obtain a simple integral expression of this operator and deduce its positi…
Atomic decomposition and weak factorization in generalized Hardy spaces of closed forms
Aline Bonami, Justin Feuto, Sandrine Grellier +1
We give an atomic decomposition of closed forms on R n , the coefficients of which belong to some Hardy space of Musielak-Orlicz type. These spaces are natural generalizations of w…
Approximations in Sobolev Spaces by Prolate Spheroidal Wave Functions
Aline Bonami, Abderrazek Karoui
Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) This is due to the promising new contributio…