Completeness of boundary traces of eigenfunctions

Xiaolong Han; Andrew Hassell; Hamid Hezari; Steve Zelditch

doi:10.1112/plms/pdv018

Completeness of boundary traces of eigenfunctions

Xiaolong Han, Andrew Hassell, Hamid Hezari, Steve Zelditch

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper, we study the boundary traces of eigenfunctions on the boundary of a smooth and bounded domain. An identity derived by Bäcker, Fürstburger, Schubert, and Steiner ['Behaviour of boundary functions for quantum billiards', J. Phys. A 35 (2002) 10293-10310], expressing (in some sense) the asymptotic completeness of the set of boundary traces in a frequency window of size O(1), is proved both for Dirichlet and Neumann boundary conditions. We then prove a semiclassical generalization of this identity.

Original language	English
Pages (from-to)	749-773
Number of pages	25
Journal	Proceedings of the London Mathematical Society
Volume	111
Issue number	3
DOIs	https://doi.org/10.1112/plms/pdv018
Publication status	Published - 29 May 2014

Access to Document

10.1112/plms/pdv018

Cite this

@article{73866bd386414f8db521e8a992f028cf,

title = "Completeness of boundary traces of eigenfunctions",

abstract = "In this paper, we study the boundary traces of eigenfunctions on the boundary of a smooth and bounded domain. An identity derived by B{\"a}cker, F{\"u}rstburger, Schubert, and Steiner ['Behaviour of boundary functions for quantum billiards', J. Phys. A 35 (2002) 10293-10310], expressing (in some sense) the asymptotic completeness of the set of boundary traces in a frequency window of size O(1), is proved both for Dirichlet and Neumann boundary conditions. We then prove a semiclassical generalization of this identity.",

author = "Xiaolong Han and Andrew Hassell and Hamid Hezari and Steve Zelditch",

note = "Publisher Copyright: {\textcopyright} 2015 London Mathematical Society.",

year = "2014",

month = may,

day = "29",

doi = "10.1112/plms/pdv018",

language = "English",

volume = "111",

pages = "749--773",

journal = "Proceedings of the London Mathematical Society",

issn = "0024-6115",

publisher = "John Wiley & Sons Ltd.",

number = "3",

}

TY - JOUR

T1 - Completeness of boundary traces of eigenfunctions

AU - Han, Xiaolong

AU - Hassell, Andrew

AU - Hezari, Hamid

AU - Zelditch, Steve

PY - 2014/5/29

Y1 - 2014/5/29

N2 - In this paper, we study the boundary traces of eigenfunctions on the boundary of a smooth and bounded domain. An identity derived by Bäcker, Fürstburger, Schubert, and Steiner ['Behaviour of boundary functions for quantum billiards', J. Phys. A 35 (2002) 10293-10310], expressing (in some sense) the asymptotic completeness of the set of boundary traces in a frequency window of size O(1), is proved both for Dirichlet and Neumann boundary conditions. We then prove a semiclassical generalization of this identity.

AB - In this paper, we study the boundary traces of eigenfunctions on the boundary of a smooth and bounded domain. An identity derived by Bäcker, Fürstburger, Schubert, and Steiner ['Behaviour of boundary functions for quantum billiards', J. Phys. A 35 (2002) 10293-10310], expressing (in some sense) the asymptotic completeness of the set of boundary traces in a frequency window of size O(1), is proved both for Dirichlet and Neumann boundary conditions. We then prove a semiclassical generalization of this identity.

UR - http://www.scopus.com/inward/record.url?scp=84941206030&partnerID=8YFLogxK

U2 - 10.1112/plms/pdv018

DO - 10.1112/plms/pdv018

M3 - Article

SN - 0024-6115

VL - 111

SP - 749

EP - 773

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 3

ER -

Completeness of boundary traces of eigenfunctions

Abstract

Access to Document

Other files and links

Fingerprint

Cite this