Browsing by Author "Koprubasi, T, Mohapatra, RN"

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A study of some discrete Dirac equations with principal functions
(2016-12-01) Koprubasi T., Mohapatra R.; Koprubasi, T, Mohapatra, RN
Let L denote the operator generated in ℓ2(N, C2) by (Formula Presented.) and the boundary condition (Formula Presented.) where (an) , (bn) , (pn) and (qn) , n∈ N are complex sequences, γi, βi∈ C, i= 0 , 1 , 2 and λ is a eigenparameter. With respect to the spectral properties of L, we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities of L, if (Formula Presented.) holds for some ε> 0 and δ∈[12,1].
An inverse scattering problem for eigenparameter-dependent discrete Dirac system with Levinson formula
(2022-01-01) Koprubasi T., Mohapatra R.N.; Koprubasi, T, Mohapatra, RN
In this paper, we have considered an inverse scattering problem for discrete Dirac operator L with eigenparameter dependent boundary condition. At the outset, the Jost solution and the Jost function of L are given. Then the zeros of the Jost function and some properties of the scattering function are examined. After.nding the scattering dataset and the main equation for the operator L, the uniqueness of the kernel, continuity of the scattering function and the appropriate Levinson type formula are obtained.
Corrigendum to "Inverse scattering problem with Levinson formula for eigenparameter-dependent discrete Sturm-Liouville equation"
(2023.01.01) Koprubasi, T, Mohapatra, RN
Inverse scattering problem with Levinson formula for eigenparameter-dependent discrete Sturm–Liouville equation
(2023-01-30) Koprubasi T., Mohapatra R.N.; Koprubasi, T, Mohapatra, RN
In this paper, an inverse scattering problem for discrete Sturm–Liouville equation with eigenparameter-dependent boundary condition is investigated. In quest of finding scattering function and the main equation of this problem, the uniqueness of the kernel is proven. Also, an appropriate Levinson-type formula based on the continuity of scattering function is given.
Spectral analysis of discrete dirac equation with generalized eigenparameter in boundary condition
(2019-01-01) Koprubasi T., Mohapatra R.; Koprubasi, T, Mohapatra, RN
Let L denote the discrete Dirac operator generated in ℓ2 (N, C 2) by the non-selfadjoint difference operators of first order { an+1 y(2) +bn+1 n y(2) n + pn y(1) n = λy(1) n an−1 y(1) +bn−1 n y(1) n + qn y(2) n = λy(2) n, n ∈ N, with boundary condition (0.1) p∑ k=0 (y (2) 1γk + y(1) 0βk) λk = 0, (0.2) where (an), (bn), (pn) and (qn), n ∈ N are complex sequences, γi, βi ∈ C, i = 0, 1, 2, …, p and λ is a eigenparameter. We discuss the spectral properties of L and we investigate the properties of the spectrum and the principal vectors corresponding to the spectral singularities of L, if ∞∑ |n|(|1 − an | + |1 + bn | +∣ ∣ ∣pn ∣∣ ∣∣∣qn ∣∣∣) + < ∞n=1 holds.
Spectral properties of generalized eigenparameter dependent discrete Sturm-Liouville type equation
(2017-07-10) Koprubasi T., Mohapatra R.N.; Koprubasi, T, Mohapatra, RN
Let L denote the non-selfadjoint diﬀerence operator of second order with boundary condition generated in ℓ2 (ℕ) by (Figure presented.) (Figure presented.) where {an}n∈ℕ and {bn}n∈ℕ are complex sequences, γi, βi ∈ ℂ, i = 0, 1, 2, …, p and λ is a eigenparameter. Discussing the spectral properties of L, we investigate the Jost function, spectrum, the spectral singularities, and the properties of the principal vectors corresponding to the spectral singularities of L, if (Figure presented.).