Djakov, Plamen Borissov and Mityagin, Boris
(2013)
*Equiconvergence of spectral decompositions of Hill–Schrödinger operators.*
Journal of Differential Equations, 255
(10).
pp. 3233-3283.
ISSN 0022-0396

Official URL: http://dx.doi.org/10.1016/j.jde.2013.07.030

## Abstract

We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator L = d(2)/dx(2) + v(x), x is an element of [0, pi], with H-per(-1)-potential and the free operator L-0 = -d(2)/dx(2), subject to periodic, antiperiodic or Dirichlet boundary conditions. In particular, we prove that
parallel to S-N - S-N(0) : L-a -> L-b parallel to -> 0 if 1 < a <= b < infinity, 1/a - 1/b < 1/2,
where S-N and S-N(0) are the N-th partial sums of the spectral decompositions of L and L-0. Moreover, if v is an element of H-alpha with 1/2 < alpha < 1 and 1/a = 3/2 - alpha, then we obtain uniform equiconvergence: parallel to S-N - S-N(0) : L-a -> L-infinity parallel to -> 0 as N -> infinity.

Item Type: | Article |
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Uncontrolled Keywords: | Hill-Schrodinger operators; Singular potentials; Spectral decompositions; Equiconvergence |

Subjects: | Q Science > QA Mathematics > QA299.6-433 Analysis |

Divisions: | Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences |

Depositing User: | Plamen Borissov Djakov |

Date Deposited: | 06 Jan 2014 15:26 |

Last Modified: | 01 Aug 2019 12:04 |

URI: | https://research.sabanciuniv.edu/id/eprint/22342 |