Ball prolate spheroidal wave functions in arbitrary dimensions
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-dim...
Saved in:
| Main Authors: | , , , |
|---|---|
| 其他作者: | |
| 格式: | Article |
| 語言: | English |
| 出版: |
2020
|
| 主題: | |
| 在線閱讀: | https://hdl.handle.net/10356/142377 |
| 標簽: |
添加標簽
沒有標簽, 成為第一個標記此記錄!
|
| 總結: | 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. |
|---|