Geodesic
Systems with nonextendable convergence of quasipolynomials
Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 728-733.

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The system $e(\Lambda)=\bigl\{(it)^ke^{i\lambda_nt}, 0\le k\le m_n-1\bigr\}_{n=1}^\infty$, where $\Lambda=\{\lambda_n\}$ is the set of zeros (of multiplicities $m_n$ ) of the Fourier transform $$ L(z)=\int_{-a}^ae^{izt}\,d\mathscr L(t) $$ of a singular Cantor-Lebesgue measure, is examined. We prove that $e(\Lambda)$ is complete and minimal in $L_p(-a,a)$, with $p\ge1$, and that $|L(x+iy)|^2$ does not satisfy the Muckenhoupt condition on any horizontal line $\operatorname{Im}z=y\ne0$ in the complex plane. This implies that $e(\Lambda)$ does not have the property of convergence extension. 
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     author = {A. A. Ryabinin},
     title = {Systems with nonextendable convergence of quasipolynomials},
     journal = {Matemati\v{c}eskie zametki},
     pages = {728--733},
     publisher = {mathdoc},
     volume = {64},
     number = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a9/}
}
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A. A. Ryabinin. Systems with nonextendable convergence of quasipolynomials. Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 728-733. http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a9/

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