اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA remark on the discrete spectrum of non-self-adjoint Jacobi operators
80
0
0.0
(
0
)
تأليف
Leonid Golinskii
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the trace class perturbations of the whole-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we refine the Lieb--Thirring inequality due to Hansmann--Katriel. The spectral enclosure for such operators is also discussed.
قيم البحث
اقرأ أيضاً
We study the trace class perturbations of the half-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we obtain the Lieb--Thirring inequalities
for such operators. The spectral enclosure for the discrete spectrum and embedded eigenvalues are also discussed.
We investigate the instability index of the spectral problem $$ -c^2y + b^2y + V(x)y = -mathrm{i} z y $$ on the line $mathbb{R}$, where $Vin L^1_{rm loc}(mathbb{R})$ is real valued and $b,c>0$ are constants. This problem arises in the study of stab
ility of solitons for certain nonlinear equations (e.g., the short pulse equation and the generalized Bullough-Dodd equation). We show how to apply the standard approach in the situation under consideration and as a result we provide a formula for the instability index in terms of certain spectral characteristics of the 1-D Schrodinger operator $H_V=-c^2frac{d^2}{dx^2}+b^2 +V(x)$.
In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.
We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.SP/0702122] and John Weir [arXiv:0711.1371].
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal usage of the Cauchy-Schwarz inequal
ity--is used to produce ``parameter-free, ``projection-free
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
