Levitin, M;
Sobolev, A;
Sobolev, D;
(2010)
On the near periodicity of eigenvalues of Toeplitz Matrices.
In: Levitin, M and Vassiliev, D, (eds.)
Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008).
American Mathematical Society
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Abstract
Let A be an infinite Toeplitz matrix with a real symbol f defined on [−π,π]. It is well known that the sequence of spectra of finite truncations AN 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 π, that the eigenvalues of AN 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 A2 in a particular case when f is a piecewise constant function taking values −1 and 1.
| Type: | Book chapter |
|---|---|
| Title: | On the near periodicity of eigenvalues of Toeplitz Matrices |
| ISBN-13: | 9780821852729 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://www.maa.org/press/maa-reviews/operator-the... |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > UCL School of Management UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1575575 |
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