2007/07/18 by Lazhar Dhaouadi, Dhaouadi, Lazhar
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.0707.2728
openalex publication_date 2007/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property [6]. They are an orthogonal basis of both L2(-1,1) and the Paley-Wiener space of bandlimited functions. They also satisfy a discrete orthogonality relation. No other system of classical orthogonal functions is known to possess this strange property. We prove that there are new systems possessing this property in q-Fourier analysis. As application we give a new sampling formula with qn as sampling points, where 0 < q < 1.