Annales Henri Poincaré

, Volume 8, Issue 2, pp 301–336

The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics


DOI: 10.1007/s00023-006-0309-1

Cite this article as:
Mantica, G. & Guzzetti, D. Ann. Henri Poincaré (2007) 8: 301. doi:10.1007/s00023-006-0309-1


We study measures generated by systems of linear iterated functions, their Fourier transforms, and those of their orthogonal polynomials. We characterize the asymptotic behaviours of their discrete and continuous averages. Further related quantities are analyzed, and relevance of this analysis to quantum mechanics is briefly discussed.

Copyright information

© Birkhäuser Verlag, Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Center for Non-linear and Complex SystemsUniversità dell’InsubriaComoItaly
  2. 2.CNISM and INFN sez.ComoItaly
  3. 3.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan