Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes

Oran Gannot

Research output: Contribution to journalArticlepeer-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.

Original languageEnglish (US)
Pages (from-to)988-1029
Number of pages42
JournalComptes Rendus Mathematique
Volume356
Issue number10
DOIs
StatePublished - Oct 2018

ASJC Scopus subject areas

  • General Mathematics

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