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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Lagrange's mean motion problem

Author: S. Yu. Favorov
Translated by: the author
Original publication: Algebra i Analiz, tom 20 (2008), nomer 2.
Journal: St. Petersburg Math. J. 20 (2009), 319-324
MSC (2000): Primary 33B10, 30B50
Published electronically: February 4, 2009
MathSciNet review: 2424001
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Abstract: The famous mean motion problem, dating back to Lagrange, is about the existence of the average speed for the amplitude of any exponential polynomial with exponents on the imaginary axis, whenever the variable moves along a horizontal line. This problem was completely solved by B. Jessen and H. Tornehave in Acta Mathematica, vol. 77, 1945. Here, we give a simple version of that proof.

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Additional Information

S. Yu. Favorov
Affiliation: Department of Mathematics, Kharkov National University, Svobody Square 4, Kharkov 61077, Ukraine

Keywords: Mean motion, exponential polynomial, Lagrange's conjecture, Weierstrass preparation theorem
Received by editor(s): August 10, 2007
Published electronically: February 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society

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