Wavelet Based Solutions to the Poisson and the Helmholtz Equations on the n-Dimensional Unit Sphere

被引：0
|
作者：
Iglewska-Nowak, Ilona [1 ]
Stefaniak, Piotr [2 ]
机构：
[1] West Pomeranian Univ Technol, Sch Math, Al Piastow 17, PL-70310 Szczecin, Poland
[2] Nicolaus Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, Poland
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2023年 / 29卷 / 03期
关键词：
Spherical wavelets; n-Spheres; PDE; Poisson equation; Helmholtz equation; PARTIAL-DIFFERENTIAL-EQUATIONS; DIRECTIONAL WAVELETS;
D O I：
10.1007/s00041-023-10008-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a method of solving partial differential equations on the n-dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate identities. We give an explicit analytical solution to the Poisson equation and to the Helmholtz equations. For the first one and for some special values of the parameter in the latter one, we derive a closed formula for the generalized Green function.
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页数：22
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