ترغب بنشر مسار تعليمي؟ اضغط هنا

Eigenvalues of Toeplitz matrices in the bulk of the spectrum

148   0   0.0 ( 0 )
 نشر من قبل Igor Krasovsky
 تاريخ النشر 2011
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

The authors analyze the asymptotics of eigenvalues of Toeplitz matrices with certain continuous and discontinuous symbols. In particular, the authors prove a conjecture of Levitin and Shargorodsky on the near-periodicity of Toeplitz eigenvalues.



قيم البحث

اقرأ أيضاً

353 - P. Deift , A. Its , I. Krasovsky 2012
We review some history and some recent results concerning Toeplitz determinants and their applications. We discuss, in particular, the crucial role of the two-dimensional Ising model in stimulating the development of the theory of Toeplitz determinants.
225 - P. Deift , A. Its , I. Krasovsky 2012
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the regular part of the symbols and obtain an estimate f or the error term in the asymptotics. Our proof is based on the Riemann-Hilbert analysis of the related systems of orthogonal polynomials and on differential identities for Toeplitz determinants. The result discussed in this paper is crucial for the proof of the asymptotics in the general case of Fisher-Hartwig singularities and extensions to Hankel and Toeplitz+Hankel determinants in [15].
205 - P. Deift , A. Its , I. Krasovsky 2009
We study the asymptotics in n for n-dimensional Toeplitz determinants whose symbols possess Fisher-Hartwig singularities on a smooth background. We prove the general non-degenerate asymptotic behavior as conjectured by Basor and Tracy. We also obtain asymptotics of Hankel determinants on a finite interval as well as determinants of Toeplitz+Hankel type. Our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the Riemann-Hilbert approach.
148 - Bo-Yan Xi , Fuzhen Zhang 2019
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.
For $alpha > 0$ we consider the operator $K_alpha colon ell^2 to ell^2$ corresponding to the matrix [left(frac{(nm)^{-frac{1}{2}+alpha}}{[max(n,m)]^{2alpha}}right)_{n,m=1}^infty.] By interpreting $K_alpha$ as the inverse of an unbounded Jacobi matrix , we show that the absolutely continuous spectrum coincides with $[0, 2/alpha]$ (multiplicity one), and that there is no singular continuous spectrum. There is a finite number of eigenvalues above the continuous spectrum. We apply our results to demonstrate that the reproducing kernel thesis does not hold for composition operators on the Hardy space of Dirichlet series $mathscr{H}^2$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا