Problèmes aux limites elliptiques pour les opérateurs de Bessel, avec applications aux espaces-temps anti-de Sitter

Oran Gannot

doi:10.1016/j.crma.2018.08.003

Problèmes aux limites elliptiques pour les opérateurs de Bessel, avec applications aux espaces-temps anti-de Sitter

Translated title of the contribution: Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes

Oran Gannot

Mathematics

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

4 Scopus citations

Abstract

This paper considers boundary value problems for a class of singular elliptic operators that appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the normal direction. After formulating a Lopatinskiı̌ condition, elliptic estimates are established for functions supported near the boundary. The Fredholm property follows from additional hypotheses in the interior. This paper provides a rigorous framework for mode analysis on aAdS spacetimes for a wide range of boundary conditions considered in the physics literature. Completeness of eigenfunctions for some Bessel operator pencils is shown.

Translated title of the contribution	Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes
Original language	French
Pages (from-to)	988-1029
Number of pages	42
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	10
DOIs	https://doi.org/10.1016/j.crma.2018.08.003
State	Published - Oct 2018

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.crma.2018.08.003

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title = "Probl{\`e}mes aux limites elliptiques pour les op{\'e}rateurs de Bessel, avec applications aux espaces-temps anti-de Sitter",

abstract = "This paper considers boundary value problems for a class of singular elliptic operators that appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the normal direction. After formulating a Lopatinski{\v ı} condition, elliptic estimates are established for functions supported near the boundary. The Fredholm property follows from additional hypotheses in the interior. This paper provides a rigorous framework for mode analysis on aAdS spacetimes for a wide range of boundary conditions considered in the physics literature. Completeness of eigenfunctions for some Bessel operator pencils is shown.",

author = "Oran Gannot",

note = "Funding Information: This paper is based on work supported by NSF grants DMS-1201417 and DMS-1500852 . I would like to thank Maciej Zworski for his encouragement on this project. Funding Information: This paper is based on work supported by NSF grants DMS-1201417 and DMS-1500852. I would like to thank Maciej Zworski for his encouragement on this project. Publisher Copyright: {\textcopyright} 2018 Acad{\'e}mie des sciences",

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month = oct,

doi = "10.1016/j.crma.2018.08.003",

language = "French",

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AB - This paper considers boundary value problems for a class of singular elliptic operators that appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the normal direction. After formulating a Lopatinskiı̌ condition, elliptic estimates are established for functions supported near the boundary. The Fredholm property follows from additional hypotheses in the interior. This paper provides a rigorous framework for mode analysis on aAdS spacetimes for a wide range of boundary conditions considered in the physics literature. Completeness of eigenfunctions for some Bessel operator pencils is shown.

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Problèmes aux limites elliptiques pour les opérateurs de Bessel, avec applications aux espaces-temps anti-de Sitter

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