Geodesic
Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions
Discrete analysis (2017) Cet article a éte moissonné depuis la source Scholastica

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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.
Publié le : 
@article{DAS_2017_a7,
     author = {Vera Mikyoung Hur and Mathew A. Johnson and Jeremy L. Martin},
     title = {Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions},
     journal = {Discrete analysis},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2017_a7/}
}
TY  - JOUR
AU  - Vera Mikyoung Hur
AU  - Mathew A. Johnson
AU  - Jeremy L. Martin
TI  - Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions
JO  - Discrete analysis
PY  - 2017
UR  - http://geodesic.mathdoc.fr/item/DAS_2017_a7/
LA  - en
ID  - DAS_2017_a7
ER  - 
%0 Journal Article
%A Vera Mikyoung Hur
%A Mathew A. Johnson
%A Jeremy L. Martin
%T Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions
%J Discrete analysis
%D 2017
%U http://geodesic.mathdoc.fr/item/DAS_2017_a7/
%G en
%F DAS_2017_a7
Vera Mikyoung Hur; Mathew A. Johnson; Jeremy L. Martin. Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions. Discrete analysis (2017). http://geodesic.mathdoc.fr/item/DAS_2017_a7/