Sign intermixing for Riesz bases and frames measured in the Kantorovich-Rubinstein norm

Nikolai Nikolski, Alexander Volberg

Published 2020-11-18Version 1

We measure a sign interlacing phenomenon for Bessel sequences $ (u_{k})$ in $ L^{2}$ spaces in terms of the Kantorovich--Rubinstein mass moving norm $ \Vert u_{k}\Vert _{KR}$. Our main observation shows that, quantitatively, the rate of the decreasing $ \Vert u_{k}\Vert _{KR}\longrightarrow 0$ havily depends on S. Bernstein $ n$-widths of a compact of Lipschitz functions. In particular, it depends on the dimension of the measure space.