Deviations of Riesz projections of Hill operators with singular potentials

Plamen Djakov; Boris Mityagin

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arXiv · 0802.2197

Deviations of Riesz projections of Hill operators with singular potentials

Plamen Djakov·Boris Mityagin

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Abstract

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. $

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BibTeX RIS

Plamen Djakov, Boris Mityagin. 2008-02-15. Deviations of Riesz projections of Hill operators with singular potentials. https://arxiv.org/abs/0802.2197

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