论文标题
通过圆形pr素球序列的Hankel Sobolev空间中的近似
Approximation in Hankel Sobolev Space by Circular prolate spheroidal series
论文作者
论文摘要
最近，随着科学的进步和特征性的特性，它区分了SLEPIAN系统，称为pr酸球状波的功能与其他正交系统的功能，很明显，它在数学统计，信号处理，数值分析等等多个领域变得重要的贡献变得很重要。 $ \ MATHCAL {H}_α^r $，$ r> 0 $和$α\ geq -1/2 $，通过$ l^2 $ norm的广义pr酸球形波函数。同时，我们将通过两个特殊功能创建上一个系统的两个统一近似值，第一个是贝塞尔函数类型，第二个是修改的jacobi多项式。此外，使用概括的PSWF是Sturm Liouville操作员的特征功能，我们将改善相关特征值的新界限。我们在这里考虑的广义倾斜基础是D. Slepian于1964年引入的圆形pr素毛球波函数（CPSWF），称为Hankel Prate，用$ \ vp $，$ c> 0 $表示。 Hankel Prate涵盖了经典的PSWFS $（α= \ pm1/2）$，为此，许多作者先前已经建立了相应的结果。
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 several areas such as mathematical statistics, signal processing, numerical analysis etc...The main issue of this work is to establish the convergence quality of the truncated error of a function $f$ from the Hankel Sobolev space $\mathcal{H}_α^r$, $r > 0$ and $α\geq -1/2$, by a generalized prolate spheroidal wave functions basis in $L^2$ norm. In the meantime, we will create two uniform approximations of the previous system by two special functions, the first is a Bessel function type and the second is a modified Jacobi polynomial. Furthermore, using the fact that the generalized PSWFs are the eigenfunctions of a Sturm Liouville operator, we will improve a new bound of the associated eigenvalues. The generalized prolate basis we consider here is the circular prolate spheroidal wave function (CPSWFs), called also Hankel prolate, introduced by D. Slepian in 1964, denoted by $\vp$, $c > 0$. The Hankel prolate covers the classical PSWFs $(α=\pm1/2)$ for which corresponding results have been established previously by many authors.
