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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 3, Pages 355–361
DOI: https://doi.org/10.4213/tmf9227 (Mi tmf9227) 		 
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
Full-text PDF (423 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf9227
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.
Funding agency Grant number
Russian Science Foundation 15-11-20007
This research is supported by a grant from the Russian Science Foundation (Project No. 15-11-20007).
Received: 15.05.2016
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 3, Pages 1712–1717
DOI: https://doi.org/10.1134/S0040577916120035
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. B. Shabat, “Functional Cantor equation”, TMF, 189:3 (2016), 355–361; Theoret. and Math. Phys., 189:3 (2016), 1712–1717
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9227
  • https://doi.org/10.4213/tmf9227
  • https://www.mathnet.ru/eng/tmf/v189/i3/p355
    • This publication is cited in the following 1 articles:
    1. A. B. Shabat, “Constructive scattering theory”, Theoret. and Math. Phys., 193:1 (2017), 1420–1428  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:498
    Full-text PDF :144
    References:88
    First page:55
     
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