Some inverse spectral results for semi-classical Schrödinger operators
نویسندگان
چکیده
منابع مشابه
global results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Inverse spectral problems for Sturm-Liouville operators with transmission conditions
Abstract: This paper deals with the boundary value problem involving the differential equation -y''+q(x)y=lambda y subject to the standard boundary conditions along with the following discontinuity conditions at a point y(a+0)=a1y(a-0), y'(a+0)=a2y'(a-0)+a3y(a-0). We develop the Hochestadt-Lieberman’s result for Sturm-Lio...
متن کاملSchrödinger Operators with Fairly Arbitrary Spectral Features
It is shown, using methods of inverse-spectral theory, that there exist Schrödinger operators on the line with fairly general spectral features. Thus, for instance, it follows from the main theorem, that if 0 < α < 1 is arbitrary, and if Σ is any perfect subset of (−∞, 0] with Hausdorff dimension α, then there exist potentials q j , j = 1, 2 such that the associated Schrödinger operators H j ar...
متن کامل[ m at h . SP ] 9 O ct 1 99 8 SPECTRAL INSTABILITY FOR SOME SCHRÖDINGER OPERATORS
We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schrödinger operators in one dimension, and apply it to the complex resonances of a typical operator with a dilation analytic potential. AMS subject classification: 34L05, 35P05, 47A75, 49R...
متن کاملSymplectic inverse spectral theory for pseudodifferential operators
We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2007
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2007.v14.n4.a7