Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions
Spectral Theory
2017-09-06 v3 Analysis of PDEs
Combinatorics
Abstract
We study oscillations in the eigenfunctions for a fractional Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1609.02189,
title = {Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions},
author = {Vera Mikyoung Hur and Mathew A. Johnson and Jeremy L. Martin},
journal= {arXiv preprint arXiv:1609.02189},
year = {2017}
}
Comments
20 pages