اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations
152
0
0.0
(
0
)
تأليف
Alexander Sakhnovich
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider canonical systems (with $2ptimes 2p$ Hamiltonians $H(x)geq 0$), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh--Weyl and spectral matrix functions and related $S$-nodes. Procedures for solving inverse problems are given.
قيم البحث
اقرأ أيضاً
We obtain high energy asymptotics of Titchmarsh-Weyl functions of the generalised canonical systems generalising in this way a seminal Gesztesy-Simon result. The matrix valued analog of the amplitude function satisfies in this case an interesting new
identity. The corresponding structured operators are studied as well.
An important representation of the general-type fundamental solutions of the canonical systems corresponding to matrix string equations is established using linear similarity of a certain class of Volterra operators to the squared integration. Explic
it fundamental solutions of these canonical systems are also constructed via the GBDT version of Darboux transformation. Examples and applications to dynamical canonical systems are given. Explicit solutions of the dynamical canonical systems are constructed as well. Three appendices are dedicated to the Weyl--Titchmarsh theory for canonical systems, transformation of a subclass of canonical systems into matrix string equations (and of a smaller subclass of canonical systems into matrix Schrodinger equations), and a linear similarity problem for Volterra operators.
We consider the inverse spectral theory of vibrating string equations. In this regard, first eigenvalue Ambarzumyan-type uniqueness theorems are stated and proved subject to separated, self-adjoint boundary conditions. More precisely, it is shown tha
t there is a curve in the boundary parameters domain on which no analog of it is possible. Necessary conditions of the $n$-th eigenvalue are identified, which allows to state the theorems. In addition, several properties of the first eigenvalue are examined. Lower and upper bounds are identified, and the areas are described in the boundary parameters domain on which the sign of the first eigenvalue remains unchanged. This paper contributes to inverse spectral theory as well as to direct spectral theory.
We continue to investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two more model examples of generalized indefinit
e strings under rather wide perturbations. In particular, one of these results allows us to prove that the absolutely continuous spectrum of the isospectral problem associated with the two-component Camassa-Holm system in a certain dispersive regime is essentially supported on the set $(-infty,-1/2]cup [1/2,infty)$.
For the Schrodinger equation $-d^2 u/dx^2 + q(x)u = lambda u$ on a finite $x$-interval, there is defined an asymmetry function $a(lambda;q)$, which is entire of order $1/2$ and type $1$ in $lambda$. Our main result identifies the classes of square-in
tegrable potentials $q(x)$ that possess a common asymmetry function. For any given $a(lambda)$, there is one potential for each Dirichlet spectral sequence.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
