Uniconvergence theorems for Sturm--Liouville operators with potentials from Sobolev space $W_2^{-1}[0,π]$
| dc.creator | Sadovnichaya, I. V. | |
| dc.date | 2008-06-18 | |
| dc.date.accessioned | 2026-07-07T09:45:23Z | |
| dc.date.available | 2026-07-07T09:45:23Z | |
| dc.description | We consider a Sturm--Liouville $Ly=-y''+q(x)y$ in space $L_2[0,π]$ with potential from Sobolev space $W_2^{-1}[0,π]$. Moreover, we assume, that $q=u'$, where $u\in L_2[0,π]$. We consider Direchlet boundary conditions $y(0)=y(π)=0$, although we can treat a boundary conditions of Sturm type. It is known, that operators of such class have a discrete spectr with only accumulation point $+\infty$ and the system $\{y_k\}_1^\infty$ of eigen and associated functions is a Riesz basis in $L_2[0,π]$. Moreover, this basis is a Hilbert--Schmidt perturbation of the basis $\{sin(kx)\}_1^\infty$. In this paper we prove the uniconvergence theorem: for any element $f\in L_2[0,π]$ the sequence $P_nf-S_nf\to0$ as $n\to\infty$ in $C[0,π]$ (here $P_n$ and $S_n$ are the Riesz projectors to $\{y_k\}_1^n$ and $\{\sin(kt)\}_1^n$ respectively). | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0806.3016 | |
| dc.identifier | http://arxiv.org/abs/0806.3016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163176 | |
| dc.subject | Spectral Theory | |
| dc.subject | Functional Analysis | |
| dc.subject | 47E05; 34L10; 34L40 | |
| dc.title | Uniconvergence theorems for Sturm--Liouville operators with potentials from Sobolev space $W_2^{-1}[0,π]$ | |
| dc.type | text |