Excesses of systems of exponential functions

A. M. Sedletskii

Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 803-814

Résumé

Conditions on the closeness of real sequences $\{\lambda_n\}$ and $\{\mu_n\}$ are studied which imply the equality of the excesses of the systems $\{\exp(i\lambda_nx)\}$ and $\{\exp(i\lambda_nx)\}$ in the space $L^2(-a,a)$. A theorem is formulated in terms of the difference of the sequences $\{\lambda_n\}$ and $\{\mu_n\}$ enumerating the functions. In the corollaries of the theorem, conditions are given in terms of the behavior of the difference $\lambda_n-\mu_n$. An example is constructed showing that the condition $\lambda_n-\mu_n\to0$ alone is not sufficient for equality of the excesses.