Bari-Markus property for Riesz projections of Hill operators with singular potentials

dc.creatorDjakov, Plamen
dc.creatorMityagin, Boris
dc.date2008-03-21
dc.date.accessioned2026-07-07T09:27:54Z
dc.date.available2026-07-07T09:27:54Z
dc.descriptionThe Hill operators $L y = - y^{\prime \prime} + v(x) y, x \in [0,π],$ with $H^{-1}$ periodic potentials, considered with periodic, antiperiodic or Dirichlet boundary conditions, have discrete spectrum, and therefore, for sufficiently large $N,$ the Riesz projections $$ P_n = \frac{1}{2πi} \int_{C_n} (z-L)^{-1} dz, \quad C_n=\{z: |z-n^2|= n\} $$ are well defined. It is proved that $$\sum_{n>N} \|P_n - P_n^0\|^2_{HS} < \infty, $$ where $P_n^0$ are the Riesz projection of the free operator and $\|\cdot\|_{HS}$ is the Hilbert--Schmidt norm.
dc.identifierhttps://arxiv.org/abs/0803.3170
dc.identifierhttp://arxiv.org/abs/0803.3170
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157267
dc.subjectSpectral Theory
dc.subject34L40, 47B06, 47E05
dc.titleBari-Markus property for Riesz projections of Hill operators with singular potentials
dc.typetext

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