Bari-Markus property for Riesz projections of Hill operators with singular potentials
| dc.creator | Djakov, Plamen | |
| dc.creator | Mityagin, Boris | |
| dc.date | 2008-03-21 | |
| dc.date.accessioned | 2026-07-07T09:27:54Z | |
| dc.date.available | 2026-07-07T09:27:54Z | |
| dc.description | The 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.identifier | https://arxiv.org/abs/0803.3170 | |
| dc.identifier | http://arxiv.org/abs/0803.3170 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157267 | |
| dc.subject | Spectral Theory | |
| dc.subject | 34L40, 47B06, 47E05 | |
| dc.title | Bari-Markus property for Riesz projections of Hill operators with singular potentials | |
| dc.type | text |