اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the Inverse Resonance Problem for Schrodinger Operators
164
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider Schrodinger operators on [0,infty) with compactly supported, possibly complex-valued potentials in L^1([0,infty)). It is known (at least in the case of a real-valued potential) that the location of eigenvalues and resonances determines the potential uniquely. From the physical point of view one expects that large resonances are increasingly insignificant for the reconstruction of the potential from the data. In this paper we prove the validity of this statement, i.e., we show conditional stability for finite data. As a by-product we also obtain a uniqueness result for the inverse resonance problem for complex-valued potentials.
قيم البحث
اقرأ أيضاً
We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems (including characterization): in terms of zeros of reflection coefficient and in terms of poles of reflection coefficients (i.e.
resonances). We prove that a potential is uniquely determined by zeros of reflection coefficients and there exist distinct potentials with the same resonances. We describe the set of isoresonance potentials. Moreover, we prove the following: 1) a zero of the reflection coefficient can be arbitrarily shifted, such that we obtain the sequence of zeros of the reflection coefficient for an other compactly supported potential, 2) the forbidden domain for resonances is estimated, 3) asymptotics of resonances counting function is determined, 4) these results are applied to canonical systems.
Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schrodinger operator with a potential of finite support are derived. This includes a careful analysis of the band edge singu
larities and allows to prove a Levinson-type theorem. The main algebraic tool are the plane wave transfer matrices.
We prove Anderson localization at the internal band-edges for periodic magnetic Schr{o}dinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of the integrated
density of states for random magnetic Schr{o}dinger operators, thereby providing the initial length-scale estimate, and a Wegner estimate, for such models.
We study the Bloch variety of discrete Schrodinger operators associated with a complex periodic potential and a general finite-range interaction, showing that the Bloch variety is irreducible for a wide class of lattice geometries in arbitrary dimens
ion. Examples include the triangular lattice and the extended Harper lattice.
We demonstrate how the Moutard transformation of two-dimensional Schrodinger operators acts on the Faddeev eigenfunctions on the zero energy level and present some explicitly computed examples of such eigenfunctions for smooth fast decaying potential
s of operators with non-trivial kernel and for deformed potentials which correspond to blowing up solutions of the Novikov-Veselov equation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
