The inverse quasiperiodic problem for a diffusion operator

Nabiev, I. M.

doi:10.1134/s1064562407040126

Cited by 25 publications

(22 citation statements)

References 3 publications

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“…The inverse spectral problem for Eq. (1.1) with p(x) ∈ W 1 2 (0, 1) and q(x) ∈ L 2 (0, 1) and under (quasi)-periodic boundary conditions or interior given data were considered in [12,14,29]. This kind of problem was considered in various studies (see [1,2,9,[11][12][13][14][15][16][25][26][27]30,32,34,35]).…”

Section: ) {λ N }mentioning

confidence: 99%

On the isospectrality of the scalar energy-dependent Schrödingerproblems

Gulsen¹,

Panakhov²

2018

Turk J Math

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In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of K(x, t) − K0(x, t) and L(x, t) − L0(x, t) by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.

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Section: ) {λ N }mentioning

confidence: 99%

On the isospectrality of the scalar energy-dependent Schrödingerproblems

Gulsen¹,

Panakhov²

2018

Turk J Math

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“…Suppose, on the contrary, that ψ = c, i.e., that the functionψ := ψ − c is not identically zero. On account of the equality h = p 0 the representations (14) and (18) for the functions c and ψ give thatψ…”

Section: Solution Of (Ip1)mentioning

confidence: 99%

“…The inverse spectral problems for (1) with p ∈ W 1 2 (0, 1) and q ∈ L 2 (0, 1) and with Robin boundary conditions were discussed by M. Gasymov and G. Guseinov in their short paper [3] of 1981 containing no proofs. Such problems were also considered in [2,4,13,14,22], but only Borg-type uniqueness results were obtained therein.…”

Section: Introductionmentioning

confidence: 99%