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
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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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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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