期刊论文

Li, Huiyuan

英文

Applied and Computational Harmonic Analysis

1063-5203

2020

48

2

539-569

10.1016/j.acha.2018.08.001

The work of this author is partially supported by the National Natural Science Foundation of China (NSFC 11671166).The research of this author is partially supported by the National Natural Science Foundation of China (NSFC 11471312 and NSFC 91430216).The research of this author is partially supported by Singapore MOE AcRF Tier 1 Grant (RG 27/15) and Singapore MOE AcRF Tier 2 Grant (MOE2017-T2-2-144).The research of this author is supported in part by the National Natural Science Foundation of China (NSFC 11471031, NSFC 91430216 and NSAF U1530401) and the U.S. National Science Foundation (DMS-1419040).

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In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order alpha > -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 co...