2007
DOI: 10.1017/s0308210506000217
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Jost solutions for a class of slowly decaying potentials

Abstract: We investigate the existence and properties of the Jost solution associated with the differential equation −y + q(x)y = λy, x 0, for a class of real-or complex-valued slowly decaying potentials q. In particular, it is shown how the traditional condition q ∈ L(R + ) for the existence of the Jost solution can be replaced by q ∈ L(R + ) for a class of potentials considered here. We also examine the asymptotics of the Titchmarsh-Weyl function for a class of real-or complex-valued slowly decaying potentials and the… Show more

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“…I. 1.3] or even under somewhat weaker assumptions [30]; however, for V of the Faddeev-Marchenko class they have some special properties. Namely, set…”
Section: Asymptotics Of Jost Solutionsmentioning
confidence: 99%
See 1 more Smart Citation
“…I. 1.3] or even under somewhat weaker assumptions [30]; however, for V of the Faddeev-Marchenko class they have some special properties. Namely, set…”
Section: Asymptotics Of Jost Solutionsmentioning
confidence: 99%
“…Throughout the paper, C 1 , C 2 , C 3 , C 4 and C 5 shall stand for the constants of proposition 2.1 and lemma 2.5. c j denote various positive numbers independent of ε, whose values might be different in different proofs and f stands for the L 2 (R)-norm of a function f . [30]. However, for V of the Faddeev-Marchenko class, they have some special properties.…”
Section: Notationmentioning
confidence: 99%