and Applied Analysis 3 2. Jost Functions of 1.3 1.4 Under the condition ∫∞ 0 x ∣ ∣q x ∣ ∣dx < ∞, 2.1 1.3 has a solution e x, λ satisfying lim x→∞ e x, λ e−iλx 1, λ ∈ C , 2.2 where C {λ : λ ∈ C, Im λ ≥ 0}. The solution e x, λ is called Jost solution of 1.3 . Note that Jost solution has a representation 19

and Applied Analysis 3 2. Jost Solution of 1.4 We will denote the solution of 1.4 satisfying the condition lim x→∞ y x, λ e−iλx 1, λ ∈ C : {λ : λ ∈ C, Imλ ≥ 0}, 2.1 by e x, λ . The solution e x, λ is called the Jost solution of 1.4 . Under the condition ∫∞ 0 x ∣ ∣q x ∣ ∣dx < ∞, 2.2 the Jost solution has a representation

where (pn) and (qn), n ∈ Z are real sequences, and λ is an eigenparameter. We find a polynomial type Jost solution of this BVP. Then we investigate the analytical properties and asymptotic behavior of the Jost solution. Using the Weyl compact perturbation theorem, we prove that a self-adjoint discrete Dirac system has a continuous spectrum filling the segment [–2, 2]. We also prove that the Dir...

In the context of metric perturbation theory for non-spinning black holes, extreme mass ratio binary (EMRB) systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial...

The asymptotic behaviour of the superpotential of general SUSY transformations for a coupled channel Hamiltonian with different thresholds is analyzed. It is shown that asymptotically the superpotential can tend to a diagonal matrix with an arbitrary number of positive and negative entries depending on the choice of the factorization solution. The transformation of the Jost matrix is generalize...

Elgiz Bairamov, Yelda Aygar, and Murat Olgun Department of Mathematics, Ankara University, Tandoğan, 06100 Ankara, Turkey Correspondence should be addressed to Elgiz Bairamov, [email protected] Received 14 September 2010; Accepted 10 November 2010 Academic Editor: Raul F. Manasevich Copyright q 2010 Elgiz Bairamov et al. This is an open access article distributed under the Creative...

This work develops scattering and spectral analysis of a discrete impulsive Sturm-Liouville equation with parameter in boundary condition. Giving the Jost solution solutions this problem, we find function problem. Discussing properties function, solutions, asymptotic behavior solution, Green resolvent operator, continuous point spectrum Finally, give an example which main results are made expli...

In this paper, we construct the new integral representation of Jost solution Sturm-Liouville equation with impuls in semi axis $[0,+\infty )$ and give type relation, examine properties Kernel function their partial derivatives $x$ $\ t$, constructed obtain differential provided by function. Finally, paper prove uniqueness determination potential scattering data.

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence of Szegő asymptotics and of Jost asymptotics for the Weyl solution. We also prove L2 convergence of Szegő asymptotics on the spectrum.