The Fourier Asymptotic of the Monodromy

  • Sebastian Klein
Part of the Lecture Notes in Mathematics book series (LNM, volume 2229)


Beyond the “basic” asymptotic of the monodromy described in the Chap.  5, which applies to all λ for which |λ| is sufficiently large resp. small, we will also need another type of asymptotic estimate that specifically relates \((M(\lambda _{k,0}))_{k\in \mathbb {Z}}\) to certain Fourier coefficients. In particular, that series is square-summable. Because of the relation to Fourier coefficients, we will call this type of asymptotic “Fourier asymptotic”. Via the Fourier asymptotic, we will prove a refinement of the basic asymptotic description of the spectral data from Chap.  6. Later, in Chap.  11, we will liberate the Fourier asymptotics for the monodromy described here from the special choice λ = λk,0.


  1. [Ben-S]
    C. Bennett, R. Sharpley, Interpolation of Operators (Academic Press, Boston, 1988)zbMATHGoogle Scholar
  2. [Gra]
    L. Grafakos, Classical Fourier Analysis, 2nd edn, (Springer, New York, 2008)zbMATHGoogle Scholar
  3. [Pö-T]
    J. Pöschel, E. Trubowitz, Inverse Spectral Theory (Academic Press, London, 1987)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sebastian Klein
    • 1
  1. 1.School of Business Informatics & MathematicsUniversity of MannheimMannheimGermany

Personalised recommendations