This article is cited in 1 paper

Functional Cantor equation

A. B. Shabat<sup>ab

a</sup> Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia
^b Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow region, Russia

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.

Received: 15.05.2016

DOI: 10.4213/tmf9227

 English version: Theoretical and Mathematical Physics, 2016, 189:3, 1712–1717

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