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arXiv · 1704.05699

Fourier series of the curl operator and Sobolev spaces

R. S. Saks
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Abstract

The properties of curl and gradient of divergence operators in the domain $G$ of three-dimensional space are described. The self-conjugacy of these operators in the subspaces $\mathbf{L}_{2}(G) $ and the basis property of the system of eigenfunctions are discussed. Exact formulas are founded for solving boundary value problems in a ball and the conditions for the decomposition of vector functions into Fourier series in eigenfunctions of the curl and the gradient of divergence operators.

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R. S. Saks. 2017-04-19. Fourier series of the curl operator and Sobolev spaces. https://arxiv.org/abs/1704.05699

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