Mathematical Notes

, Volume 62, Issue 2, pp 172–180 | Cite as

On a transformation operator

  • I. M. Guseinov
Article

Abstract

We prove the existence of a transformation operator that takes the solution of the equationy″=λ2ny to the solution of the equation
$$y'' - \left( {q_0 (x) + \lambda q_1 (x) + \cdots + \lambda ^{n - 1} q_{n - 1} (x)} \right)y = \lambda ^{2n} y$$

with a condition at infinity. Some properties of the kernel of this operator are studied.

Key words

second-order ordinary differential equations Sturm-Liouville operator inverse scattering problem transformation operator 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • I. M. Guseinov
    • 1
  1. 1.M. A. Rasulzade Baku State UniversityBakuUSSR

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