Equiconvergence of spectral decompositions of Hill operators

Warning The system is temporarily closed to updates for reporting purpose.

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)

Full text not available from this repository. (Request a copy)

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

Actions (login required)

View Item
View Item