Mathematics – Spectral Theory
Scientific paper
2010-06-12
Mathematics
Spectral Theory
10 pages, 5 figures, to appear in AMS Transl. volume dedicated to tne memory of Viktor Lidskii
Scientific paper
Let $A$ be an infinite Toeplitz matrix with a real symbol $f$ defined on $[-\pi, \pi]$. It is well known that the sequence of spectra of finite truncations $A_N$ of $A$ converges to the convex hull of the range of $f$. Recently, Levitin and Shargorodsky, on the basis of some numerical experiments, conjectured, for symbols $f$ with two discontinuities located at rational multiples of $\pi$, that the eigenvalues of $A_N$ located in the gap of $f$ asymptotically exhibit periodicity in $N$, and suggested a formula for the period as a function of the position of discontinuities. In this paper, we quantify and prove the analog of this conjecture for the matrix $A^2$ in a particular case when $f$ is a piecewise constant function taking values $-1$ and $1$.
Levitin Michael
Sobolev Alexander V.
Sobolev Daphne
No associations
LandOfFree
On the near periodicity of eigenvalues of Toeplitz matrices 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 On the near periodicity of eigenvalues of Toeplitz matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the near periodicity of eigenvalues of Toeplitz matrices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-645002