Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions

Vera Mikyoung Hur, Mathew A. Johnson, Jeremy L. Martin

Research output: Contribution to journalArticlepeer-review


We study oscillations in the eigenfunctions for a fractional Schrödinger operator on the real line. An argument in the spirit of Courant's nodal domain theorem applies to an associated local problem in the upper half plane and provides a bound on the number of nodal domains for the extensions of the eigenfunctions. Using the combinatorial properties of noncrossing partitions, we turn the nodal domain bound into an estimate for the number of sign changes in the eigenfunctions. We discuss applications in the periodic setting and the Steklov problem on planar domains.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalDiscrete Analysis
Issue number2017
StatePublished - 2017


  • Eigenfunction
  • Fractional Schrödinger
  • Noncrossing partition
  • Oscillation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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