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Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions
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E.Yu. Derevtsov
Published/Copyright:
May 31, 2007
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.
Key Words: vector field,; harmonic field,; spherical harmonics,; ridge function,; Helmholtz–Hodge decomposition,; Zernike polynomials,; Funk–Hecke theorem.
Published Online: 2007-05-31
Published in Print: 2007-04-19
Copyright 2007, Walter de Gruyter
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Keywords for this article
vector field,;
harmonic field,;
spherical harmonics,;
ridge function,;
Helmholtz–Hodge decomposition,;
Zernike polynomials,;
Funk–Hecke theorem.
Articles in the same Issue
- Standard errors and confidence intervals in inverse problems: sensitivity and associated pitfalls
- Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions
- A numerical method to solve an acoustic inverse scattering problem involving ghost obstacles
- On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in L2
- Computation of discontinuous solutions of 2D linear ill-posed integral equations via adaptive grid regularization
- International Conferences Inverse Problems: Modeling and Simulation (Fethiye-Turkey), 2002, 2004, 2006
- International Conference Inverse and Ill-Posed Problems of Mathematical Physics dedicated to Professor M. M. Lavrent'ev on the occasion of his 75-th birthday August 20–25, 2007, Novosibirsk, Russia
