Geodesic
Interpolation sequences and nonspanning systems of exponentials on curves
Sbornik. Mathematics, Tome 212 (2021) no. 5, pp. 655-675

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Interpolation sequences of the form $\{\pm\lambda_n\}$ $(\lambda_n > 0)$ are investigated, and also the problem of when the system of exponentials $\{e^{\pm\lambda_n z}\}$ is nonspanning on the family of arbitrary rectifiable curves in the uniform norm. In terms of the interpolation nodes (or equivalently, the exponents of the system of exponentials) a criterion for the interpolation problem to be solvable is established and the strong nonspanning property of $\{e^{\pm\lambda_n z}\}$ is proved. This significantly improves some known results, in particular, results due to Korevaar, Dixon and Berndtsson. Bibliography: 23 titles.
Keywords: $\overline{\partial}$-problem, strong nonspanning property of a systems of exponentials
Mots-clés : interpolation sequence, majorant in the convergence class. 
@article{SM_2021_212_5_a2,
     author = {R. A. Gaisin},
     title = {Interpolation sequences and nonspanning systems of exponentials on curves},
     journal = {Sbornik. Mathematics},
     pages = {655--675},
     publisher = {mathdoc},
     volume = {212},
     number = {5},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_5_a2/}
}
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R. A. Gaisin. Interpolation sequences and nonspanning systems of exponentials on curves. Sbornik. Mathematics, Tome 212 (2021) no. 5, pp. 655-675. http://geodesic.mathdoc.fr/item/SM_2021_212_5_a2/