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Funktsional'nyi Analiz i ego Prilozheniya, 2016, Volume 50, Issue 3, Pages 81–85
DOI: https://doi.org/10.4213/faa3249 (Mi faa3249) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

Stark–Wannier ladders and cubic exponential sums

F. Kloppab, A. A. Fedotovc

a Institut de Mathématiques de Jussieu — Paris Rive Gauche
b Université Pierre et Marie Curie, Paris, France
c St. Petersburg State University, St. Petersburg, Russia
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DOI: https://doi.org/10.4213/faa3249
Abstract: Given a one-dimensional Stark–Wannier operator, we study the reflection coefficient and its poles in the lower half of the complex plane far from the real axis. In particular, the reflection coefficient is described asymptotically in terms of regularized infinite cubic exponential sums.
Keywords: Stark–Wannier ladders, cubic exponential sums.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00760
Engineering and Physical Sciences Research Council EP/K032208/1
Simons Foundation
The present work was supported by the RFBR grant 14-01-00760-a. A. F. also acknowledges the support of the Fondation Sciences Mathématiques de Paris, and F. K. acknowledges the support of the Chebyshev Laboratory and the French Embassy in Russia through the Lamé chair. Both authors acknowledge the support of the Simons foundation and the hospitality of the Isaac Newton Institute, Cambridge (UK), where this work was completed as a part of the program “Periodic and ergodic spectral problems” (supported by the grant EPSRC/EP/K032208/1).
Received: 06.11.2015
English version:
Functional Analysis and Its Applications, 2016, Volume 50, Issue 3, Pages 223–236
DOI: https://doi.org/10.1007/s10688-016-0152-1
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
Language: Russian
Citation: F. Klopp, A. A. Fedotov, “Stark–Wannier ladders and cubic exponential sums”, Funktsional. Anal. i Prilozhen., 50:3 (2016), 81–85; Funct. Anal. Appl., 50:3 (2016), 223–236
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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