F. Klopp, A. A. Fedotov, “Stark–Wannier ladders and cubic exponential sums”, Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 3,Pages <nobr>81

This article is cited in 2 papers

Brief communications

Stark–Wannier ladders and cubic exponential sums

F. Klopp^ab, A. A. Fedotov^c

^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

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.

UDC: 517.984.5

Received: 06.11.2015

DOI: 10.4213/faa3249