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Theoretical and Mathematical Physics

, Volume 189, Issue 3, pp 1712–1717 | Cite as

Functional Cantor equation

  • A. B. Shabat
Article

Abstract

We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.

Keywords

inverse scattering problem Fourier–Stieltjes integral q-difference equation 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASMoscowRussia
  2. 2.Institute of Mathematics with Computer Center, Ufa Science CenterRASUfaRussia

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