Geodesic
On approximation of curves by level curves of homogeneous polynomials, and on series in homogeneous polynomials
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 403-411 
È. È. Shnol'. On approximation of curves by level curves of homogeneous polynomials, and on series in homogeneous polynomials. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 403-411. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a7/
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     title = {On approximation of curves by level curves of homogeneous polynomials, and on series in homogeneous polynomials},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions are found that are necessary and sufficient for a curve $r=R(\varphi)$ to bound the domain of convergence of a series $\sum P_n(x_1,x_2)$ in homogeneous polynomials. The conditions have a nonlocal character and can be expressed in terms of the Fourier coefficients of the Fourier coefficients of $R(\varphi)$.

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