Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/142377
Title: Ball prolate spheroidal wave functions in arbitrary dimensions
Authors: Zhang, Jing
Li, Huiyuan
Wang, Li-Lian
Zhang, Zhimin
Keywords: Science::Mathematics
Issue Date: 2018
Source: Zhang, J., Li, H., Wang, L.-L., & Zhang, Z. (2020). Ball prolate spheroidal wave functions in arbitrary dimensions. Applied and Computational Harmonic Analysis, 48(2), 539-569. doi:10.1016/j.acha.2018.08.001
Journal: Applied and Computational Harmonic Analysis
Abstract: In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order α>−1 on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both an integral operator, and a Sturm–Liouville differential operator. Different from existing works on multi-dimensional PSWFs, the ball PSWFs are defined as a generalization of orthogonal ball polynomials in primitive variables with a tuning parameter c>0, through a “perturbation” of the Sturm–Liouville equation of the ball polynomials. From this perspective, we can explore some interesting intrinsic connections between the ball PSWFs and the finite Fourier and Hankel transforms. We provide an efficient and accurate algorithm for computing the ball PSWFs and the associated eigenvalues, and present various numerical results to illustrate the efficiency of the method. Under this uniform framework, we can recover the existing PSWFs by suitable variable substitutions.
URI: https://hdl.handle.net/10356/142377
ISSN: 1063-5203
DOI: 10.1016/j.acha.2018.08.001
Rights: © 2018 Elsevier Inc. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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