On Algebras of Three-Dimensional Quaternion Harmonic Fields

被引：0
|
作者：
Belishev M.I. [1 ]
机构：
[1] St. Petersburg State University, St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg
来源：
Journal of Mathematical Sciences | 2017年 / 226卷 / 6期
基金：
俄罗斯基础研究基金会;
关键词：
D O I：
10.1007/s10958-017-3559-1
中图分类号：
学科分类号：
摘要：
A quaternion field is a pair p = {α, u} of a function α and a vector field u given on a 3d Riemannian manifold Ω with boundary. A field is said to be harmonic if ∇α = rot u in Ω. The linear space of harmonic fields is not an algebra with respect to quaternion multiplication. However, it may contain commutative algebras, which is the subject of the paper. Possible applications of these algebras to the impedance tomography problem are touched upon. © 2017, Springer Science+Business Media, LLC.
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页码：701 / 710
页数：9
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