This paper deals with the construction of orthogonal polynomial bases for particular subspaces of vector fields defined in the unit ball of ℝ3. Our approach uses vector spherical harmonics to construct orthogonal sets of specific solenoidal and potential vector fields by means of ridge functions. It is shown that the approach leads to bases according to the subspaces induced by the Helmholtz–Hodge decomposition of square integrable vector fields.
Editor-in-Chief: Kabanikhin, Sergey I.
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Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions
11. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia.
2Email: dert@math.nsc.ru
32. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia.
4Email: kazan@math.nsc.ru
53. Helmut Schmidt University, Department of Mechanical Engineering, PO Box 70 08 22, 22008 Hamburg, Germany.
6Email: schuster@hsu-hh.de
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 1, Pages 19–55, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2007.002, May 2007
Publication History:
- Published Online:
- 2007-05-31
Key Words: vector field,; harmonic field,; spherical harmonics,; ridge function,; Helmholtz–Hodge decomposition,; Zernike polynomials,; Funk–Hecke theorem.
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