Related papers: Expansion into Clifford Prolate Spheroidal Wave Fu…
In the present paper, we introduce the multidimensional Clifford prolate spheroidal wave functions (CPSWFs) defined on the unit ball as eigenfunctions of a Clifford differential operator and provide a Galerkin method for their computation…
For fixed $c,$ the Prolate Spheroidal Wave Functions (PSWFs) $\psi_{n, c}$ form a basis with remarkable properties for the space of band-limited functions with bandwidth $c$. They have been largely studied and used after the seminal work of…
In this work, we first give some mathematical preliminaries concerning the generalized prolate spheroidal wave function (GPSWFs). These set of special functions have been introduced in [16] and [7] and they are defined as the infinite and…
For fixed $c,$ the Prolate Spheroidal Wave Functions (PSWFs) $\psi_{n, c}$ form a basis with remarkable properties for the space of band-limited functions with bandwidth $c$. They have been largely studied and used after the seminal work of…
In this work, we first give some mathematical preliminairies concerning the generelized prolate spheroidal wave functions(GPSWFs). This set of special functions have been introduced in [21]and [13] and they are defined as the infinite and…
For fixed $c,$ Prolate Spheroidal Wave Functions (PSWFs), denoted by $\psi_{n, c},$ form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith $c$. They have been largely studied and used after…
Prolate spheroidal wave functions (PSWFs) play an important role in various areas, from physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). One of the principal reasons for the importance of…
The main result of this thesis is an efficient protocol to determine the frequencies of a signal $C(t)= \sum_k |a_k|^2 e^{i \omega_k t}$, which is given for a finite time, to a high degree of precision. Specifically, we develop a theorem…
For a fixed reals $c>0$, $a>0$ and $\alpha>-\frac{1}{2}$, the circular prolate spheroidal wave functions (CPSWFs) or 2d-Slepian functions as some authors call it, are the eigenfunctions of the finite Hankel transform operator, denoted by…
Prolate spheroidal wave functions (PSWFs) play an important role in various areas, from physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). Even though the significance of PSWFs was realized…
We develop some properties and the Bonnet formula for Clifford Gegenbauer polynomials. Then after we define and construct weighted Clifford prolate spheroidal wave functions. We then prove that they are orthogonal in a weighted function…
Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) $\psi_{n, c},\, c>0.$ This is due to the promising new contributions of these functions in various classical as well as…
As demonstrated by Slepian et. al. in a sequence of classical papers, prolate spheroidal wave functions (PSWFs) provide a natural and efficient tool for computing with bandlimited functions defined on an interval. Recently, PSWFs have been…
In this paper we aim to give various explicit and local estimates of ball prolate spheroidal wave functions defined in [25] as eigenfunctions of both finite Fourier transform and some differential operator. In particular, we give further…
As demonstrated by Slepian et. al. in a sequence of classical papers, prolate spheroidal wave functions (PSWFs) provide a natural and efficient tool for computing with bandlimited functions defined on an interval. As a result, PSWFs are…
Recently, with the progress of science and the characteristic properties that distinguish the Slepian system called Prolate spheroidal wave functions from the others orthonormal systems, it became clear its important contributions in…
In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight…
Since the early 1960s, the fields of signal processing, data transmission, channel equalisation, filter design and others have been technologically developed and modernised as a result of the research carried out by D. Slepian and his…
In this work, we first give various explicit and local estimates of the eigenfunctions of a perturbed Jacobi differential operator. These eigenfunctions generalize the famous classical prolate spheroidal wave functions (PSWFs), founded in…
Generalized prolate spheroidal functions (GPSFs) arise naturally in the study of bandlimited functions as the eigenfunctions of a certain truncated Fourier transform. In one dimension, the theory of GPSFs (typically referred to as prolate…