Interpolation sequences and nonspanning systems of exponentials on curves

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.