Commuting difference operators and the combinatorial Gale transform

I. M. Krichever

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We develop the spectral theory of n-periodic strictly triangular difference operators L = T-k-1 + ∑j=1 k ai jT−j and the spectral theory of the “superperiodic” operators for which all solutions of the equation (L + 1)ψ = 0 are (anti)periodic. We show that, for a superperiodic operator L of order k+1, there exists a unique superperiodic operator L of order n-k-1 which commutes with L and show that the duality L ↔ L coincides, up to a certain involution, with the combinatorial Gale transform recently introduced in [21].

Original languageEnglish
Pages (from-to)175-188
Number of pages14
JournalFunctional Analysis and its Applications
Volume49
Issue number3
DOIs
Publication statusPublished - 25 Jul 2015

Keywords

  • commuting difference operators
  • frieze patterns
  • Gale transform
  • moduli spaces of n-gons
  • spectral theory of linear difference operators

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