Deviations of Riesz projections of Hill operators with singular potentials
Abstract
Description
It is shown that the deviations $P_n -P_n^0$ of Riesz projections $$
P_n = \frac{1}{2πi} \int_{C_n} (z-L)^{-1} dz, \quad C_n=\{|z-n^2|= n\}, $$ of Hill operators $L y = - y^{\prime \prime} + v(x) y, x \in [0,π],$ with zero and $H^{-1}$ periodic potentials go to zero as $n \to \infty $ even if we consider $P_n -P_n^0$ as operators from $L^1$ to $L^\infty. $ This implies that all $L^p$-norms are uniformly equivalent on the Riesz subspaces $Ran P_n. $