2018/05/27 by NourElHouda Bourguiba, Bourguiba, NourElHouda, Ahmed Souabni +1
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Elasticity and Material Modeling #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1805.10659
openalex publication_date 2018/05/27 · openalex created_date 2023/01/25 · openalex updated_date 2026/07/28
In this work, we first give some mathematical preliminaries concerning the\ngeneralized prolate spheroidal wave function (GPSWFs). These set of special\nfunctions have been introduced in [16] and [7] and they are defined as the\ninfinite and countable set of the eigenfunctions of a weighted finite Fourier\ntransform operator. Then, we show that the set of the singular values of this\noperator decay at a super-exponential decay rate. We also give some local\nestimates and bounds of these GPSWFs. As a first application of the spectral\nproperties of the GPSWFs and their associated eigenvalues, we give their\nquality of approximation in a periodic Sobolev space. Our second application is\nrelated to a generalization in the context of the GPSWFs, of the Landau-Pollak\napproximate dimension of the space of band-limited and almost time-limited\nfunctions, given in the context of the classical PSWFs, the eigenfunctions of\nthe finite Fourier transform operator. Finally, we provide the reader with some\nnumerical examples that illustrate the different results of this work.\n