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This article is cited in 1 scientific paper (total in 1 paper)
Functional Cantor equation
A. B. Shabatab a 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
Citation:
A. B. Shabat, “Functional Cantor equation”, TMF, 189:3 (2016), 355–361; Theoret. and Math. Phys., 189:3 (2016), 1712–1717
Linking options:
https://www.mathnet.ru/eng/tmf9227https://doi.org/10.4213/tmf9227 https://www.mathnet.ru/eng/tmf/v189/i3/p355
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