On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds
Abstract 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 ∇&a...
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2019
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oai:scielo:S0719-064620190001000012019-08-09On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifoldsBelishev,M. I.Vakulenko,A. F. 3d quaternion harmonic fields real uniform Banach algebras StoneWeierstrass type theorem on density uniqueness theorems. Abstract 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 (Ω) of harmonic fields is a subspace of the Banach algebra 𝒞 (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 ∨(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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.21 n.1 20192019-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000100001en10.4067/S0719-06462019000100001 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
3d quaternion harmonic fields real uniform Banach algebras StoneWeierstrass type theorem on density uniqueness theorems. |
| spellingShingle |
3d quaternion harmonic fields real uniform Banach algebras StoneWeierstrass type theorem on density uniqueness theorems. Belishev,M. I. Vakulenko,A. F. On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds |
| description |
Abstract 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 (Ω) of harmonic fields is a subspace of the Banach algebra 𝒞 (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 ∨(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. |
| author |
Belishev,M. I. Vakulenko,A. F. |
| author_facet |
Belishev,M. I. Vakulenko,A. F. |
| author_sort |
Belishev,M. I. |
| title |
On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds |
| title_short |
On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds |
| title_full |
On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds |
| title_fullStr |
On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds |
| title_full_unstemmed |
On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds |
| title_sort |
on algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2019 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000100001 |
| work_keys_str_mv |
AT belishevmi onalgebraicanduniquenesspropertiesofharmonicquaternionfieldson3dmanifolds AT vakulenkoaf onalgebraicanduniquenesspropertiesofharmonicquaternionfieldson3dmanifolds |
| _version_ |
1714206801683021824 |