Geodesic
Interpolation by periods in a~planar domain
Algebra i analiz, Tome 28 (2016) no. 5, pp. 61-170.

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Let $\Omega \subset \mathbb {R}^2$ be a countably connected domain. With any closed differential form of degree $1$ in $\Omega$ with components in $L^2(\Omega )$ one associates the sequence of its periods around the holes in $\Omega$, that is around the bounded connected components of $\mathbb R^2\setminus \Omega$. For which $\Omega$ the collection of such period sequences coincides with $\ell ^2$? We give an answer in terms of metric properties of holes in $\Omega$.
Keywords: Infinitely-connected domain, periods of forms, interpolation, Riesz basis, harmonic functions. 
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M. B. Dubashinskiǐ. Interpolation by periods in a~planar domain. Algebra i analiz, Tome 28 (2016) no. 5, pp. 61-170. http://geodesic.mathdoc.fr/item/AA_2016_28_5_a2/

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