| dc.creator | M.I. Belishev | |
| dc.creator | A.F. Vakulenko | |
| dc.date | 2019-04-01 | |
| dc.identifier | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2115 | |
| dc.identifier | 10.4067/S0719-06462019000100001 | |
| dc.description | Let Ω be a smooth compact oriented 3-dimensional Riemannian manifold with boundary. A quaternion field is a pair q = {α, u} of a function α and a vector field u on Ω. A field q is harmonic if α, u are continuous in Ω and ∇α = rot u, div u = 0 holds into Ω. The space 𝒞(Ω) of harmonic fields is a subspace of the Banach algebra 𝒬 (Ω) of continuous quaternion fields with the point-wise multiplication qq′ = {αα′ − u · u ′ , αu′ + α ′u + u ∧ u ′ }. We prove a Stone-Weierstrass type theorem: the subalgebra ∨𝒞(Ω) generated by harmonic fields is dense in 𝒬 (Ω). Some results on 2-jets of harmonic functions and the uniqueness sets of harmonic fields are provided. Comprehensive study of harmonic fields is motivated by possible applications to inverse problems of mathematical physics. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2115/1880 | |
| dc.source | CUBO, A Mathematical Journal; Vol. 21 No. 1 (2019); 01–19 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 21 Núm. 1 (2019); 01–19 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | 3d quaternion harmonic fields, real uniform Banach algebras | en-US |
| dc.subject | Stone- Weierstrass type theorem on density | en-US |
| dc.subject | uniqueness theorems | en-US |
| dc.title | On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
