Inverse spectral theory for Sturm-Liouville operators with distributional potentials
نویسندگان
چکیده
منابع مشابه
Inverse spectral theory for Sturm-Liouville operators with distributional potentials
We discuss inverse spectral theory for singular differential operators on arbitrary intervals (a, b) ⊆ R associated with rather general differential expressions of the type τf = 1 r ( − ( p[f ′ + sf ] )′ + sp[f ′ + sf ] + qf ) , where the coefficients p, q, r, s are Lebesgue measurable on (a, b) with p−1, q, r, s ∈ Lloc((a, b); dx) and real-valued with p 6= 0 and r > 0 almost everywhere on (a, ...
متن کاملInverse 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 کاملWeyl–titchmarsh Theory for Sturm–liouville Operators with Distributional Potentials
We systematically develop Weyl–Titchmarsh theory for singular differential operators on arbitrary intervals (a, b) ⊆ R associated with rather general differential expressions of the type τf = 1 r ( − ( p[f ′ + sf ] )′ + sp[f ′ + sf ] + qf ) , where the coefficients p, q, r, s are real-valued and Lebesgue measurable on (a, b), with p 6= 0, r > 0 a.e. on (a, b), and p−1, q, r, s ∈ Lloc((a, b); dx...
متن کاملWeyl–titchmarsh Theory for Sturm–liouville Operators with Distributional Coefficients
We systematically develop Weyl–Titchmarsh theory for singular differential operators on arbitrary intervals (a, b) ⊆ R associated with rather general differential expressions of the type
متن کاملSpectral loci of Sturm–Liouville operators with polynomial potentials
We consider differential equations −y+P (z, a)y = λy, where P is a polynomial of the independent variable z depending on a parameter a. The spectral locus is the set of (a, λ) such that the equation has a non-trivial solution tending to zero on two fixed rays in the complex plane. We study the topology of the spectral loci for polynomials P of degree 3 or 4 with respect to z. MSC: 81Q05, 34M60,...
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: Journal of the London Mathematical Society
سال: 2013
ISSN: 0024-6107
DOI: 10.1112/jlms/jdt041