اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSpectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
249
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider a class of Jacobi matrices with periodically modulated diagonal in a critical hyperbolic (double root) situation. For the model with non-smooth matrix entries we obtain the asymptotics of generalized eigenvectors and analyze the spectrum. In addition, we reformulate a very helpful theorem from a paper of Janas and Moszynski in its full generality in order to serve the needs of our method.
قيم البحث
اقرأ أيضاً
We consider a class of Jacobi matrices with unbounded entries in the so called critical (double root, Jordan box) case. We prove a formula for the spectral density of the matrix which relates its spectral density to the asymptotics of orthogonal polynomials associated with the matrix.
We prove new spectral enclosures for the non-real spectrum of a class of $2times2$ block operator matrices with self-adjoint operators $A$ and $D$ on the diagonal and operators $B$ and $-B^*$ as off-diagonal entries. One of our main results resembles
Gershgorins circle theorem. The enclosures are applied to $J$-frame operators.
For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we develop a met
hod for obtaining uniform asymptotics, with respect to the spectral parameter, of the generalized eigenvectors. Our technique can be applied to a wide range of Jacobi matrices.
We consider a new class of non-self-adjoint matrices that arise from an indefinite self-adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum
is qualitatively different when a certain parameter $c$ equals $0$, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of $c$.
We consider a symmetric block operator spectral problem with two spectral parameters. Under some reasonable restrictions, we state localisation theorems for the pair-eigenvalues and discuss relations to a class of non-self-adjoint spectral problems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
