A Ne Bessel Sequences and Nikishin's Example

V. A. Mironov, A. M. Sarsenbi, P. A. Terekhin

We study affine Bessel sequences in connection with the spectral theory and the multishift structure in Hilbert space. We construct a non-Besselian affine system $\{u_n(x)\}^\infty_{n=0}$ generated by continuous periodic function $u(x)$. The result is based on Nikishin's example concerning convergence in measure. We also show that affine systems $\{u_n(x)\}^\infty_{n=0}$ generated by any Lipchitz function $u(x)$ are Besselian.