ANALYSIS OF SPECTRAL APPROXIMATIONS USING PROLATE SPHEROIDAL WAVE FUNCTIONS

被引：0

作者：

Wang, Li-Lian ^{[1
]}

机构：

[1] Nanyang Technol Univ, Div Math Sci, Sch Phys & Math Sci, Singapore 637371, Singapore

来源：

MATHEMATICS OF COMPUTATION | 2010年 / 79卷 / 270期

关键词：

Prolate spheroidal wave functions; bandlimited functions; approximations in Sobolev spaces; spectral methods; quasi-uniform grids; DIFFERENTIATION; QUADRATURE; ELEMENT;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for elliptic-type equations. Illustrative numerical results consistent with the theoretical analysis are also presented.

引用

页码：807 / 827

页数：21

共 50 条

[41] Ball prolate spheroidal wave functions in arbitrary dimensions
Zhang, Jing
Li, Huiyuan
Wang, Li-Lian
Zhang, Zhimin
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2020, 48 (02) : 539 - 569
[42] DISCRETE PROLATE SPHEROIDAL WAVE-FUNCTIONS AND INTERPOLATION
DELSARTE, P
JANSSEN, AJEM
VRIES, LB
SIAM JOURNAL ON APPLIED MATHEMATICS, 1985, 45 (04) : 641 - 650
[43] A generalization of the prolate spheroidal wave functions with applications to sampling
Moumni, Tahar
Zayed, Ahmed I.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2014, 25 (06) : 433 - 447
[44] CALCULATION OF PROLATE SPHEROIDAL WAVE-FUNCTIONS - REPLY
VILENCHIK, LS
TELECOMMUNICATIONS AND RADIO ENGINEERING, 1990, 45 (12) : 149 - 150
[45] A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions
Ghaffari, Hamed Baghal
Hogan, Jeffrey A.
Lakey, Joseph D.
2019 13TH INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), 2019,
[46] Constructing prolate spheroidal quaternion wave functions on the sphere
Morais, Joao
Kou, Kit Ian
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (14) : 3961 - 3978
[47] FINITE SUMS OF PROLATE SPHEROIDAL WAVE-FUNCTIONS
PALMA, C
WAVE ELECTRONICS, 1979, 3 (04): : 311 - 317
[48] Uncertainty Principles, Prolate Spheroidal Wave Functions, and Applications
Karoui, Abderrazek
RECENT DEVELOPMENTS IN FRACTALS AND RELATED FIELDS, 2010, : 165 - 190
[49] SOME ASYMPTOTIC EXPANSIONS FOR PROLATE SPHEROIDAL WAVE FUNCTIONS
SLEPIAN, D
JOURNAL OF MATHEMATICS AND PHYSICS, 1965, 44 (02): : 99 - +
[50] CALCULATION OF PROLATE SPHEROIDAL WAVE-FUNCTIONS - REMARKS
SUCHILIN, VA
TELECOMMUNICATIONS AND RADIO ENGINEERING, 1990, 45 (12) : 150 - 150

← 1 2 3 4 5 →