On the Markov sequence problem for Jacobi polynomials

Eric A. Carlen, Jeffrey S. Geronimo, Michael Loss

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We give a simple and entirely elementary proof of Gasper's Theorem on the Markov sequence problem for Jacobi polynomials. It is based on the spectral analysis of an operator that arises in the study of a probabilistic model of colliding molecules introduced by Marc Kac, and the methods developed here yield new estimates relevant to the collision model.

Original languageEnglish (US)
Pages (from-to)3426-3466
Number of pages41
JournalAdvances in Mathematics
Issue number4
StatePublished - Mar 1 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Gasper's theorem
  • Jacobi polynomials
  • Kac model
  • Markov operators
  • Markov sequences


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