Equiconvergence theorems for Sturm--Liouville operators with distribution potentials^ the rate of equiconvergence

Details Equiconvergence theorems for Sturm--Liouville operators with distribution potentials^ the rate of equiconvergence Equiconvergence theorems for Sturm--Liouville operators with distribution potentials^ the rate of equiconvergence

2008-03-21

arxiv.org/abs/0803.3166v1

Mathematics

Spectral Theory

11 pages

Scientific paper

We consider a Sturm--Liouville operator $Ly=-y''+qy$ in $L_2[0,\pi]$ with Dirichlet boundary conditions. We assume, that the potential $q$ is complex valued and belongs to Sobolev space $W_2^\theta[0,\pi]$, $\theta\in(-1,-1/2$. This operators were successfully defined in papers of Savchuk A.M. and Shkalikov A.A. There were also shown, that theese operators have a discrete spectrum, which we denote by $\{\lambda_n\}$, and $\lim\lambda_n=+\infty$. All but finitely many of them are simple. The eigenfunctions form the Riesz basis in $L_2[0,\pi]$. We investigate a uniform on $[0,\pi]$ equiconvergence of series for this system and for trigonometric system $\{\sin(nt)\}_1^\infty$. We obtain not only a theorems of equiconvergence, but also estimate a rate of this equiconvergence.

Affiliated with

Also associated with

No associations

Rating

Equiconvergence theorems for Sturm--Liouville operators with distribution potentials^ the rate of equiconvergence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equiconvergence theorems for Sturm--Liouville operators with distribution potentials^ the rate of equiconvergence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equiconvergence theorems for Sturm--Liouville operators with distribution potentials^ the rate of equiconvergence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-587353