Djakov, Plamen Borissov and Mityagin, Boris Samuel
(2012)
*Equiconvergence of spectral decompositions of Hill operators.*
Doklady Mathematics (English) / Doklady Akademii Nauk (Russian), 86
(1).
pp. 542-544.
ISSN 1064-5624 (Print) 1531-8362 (Online)

Official URL: http://dx.doi.org/10.1134/S1064562412040333

## Abstract

We study in various functional spaces the equiconvergence of spectral decompositions of the Hill operator L = -d (2)/dx (2) + v(x), x a L (1)([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 a H (-alpha) with 1/2 < alpha < 1 and , then we obtain the uniform equiconvergence aEuro-S (N) -S (N) (0) : L (a) -> L (a)aEuro- -> 0 as N -> a.

Item Type: | Article |
---|---|

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: | 20 Oct 2012 17:14 |

Last Modified: | 31 Jul 2019 11:26 |

URI: | https://research.sabanciuniv.edu/id/eprint/19688 |