Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

Top downloads over the last seven days

A new ellipsoid associated with convex bodiesErwin Lutwak, Deane Yang, and Gaoyong ZhangVolume 104, Number 3 (2000)
The eigencurve over the boundary of weight spaceRuochuan Liu, Daqing Wan, and Liang XiaoVolume 166, Number 9 (2017)
Zeros of principal $L$ -functions and random matrix theoryZeév Rudnick and Peter SarnakVolume 81, Number 2 (1996)
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Quiver varieties and Kac-Moody algebrasHiraku NakajimaVolume 91, Number 3 (1998)
  • ISSN: 0012-7094 (print), 1547-7398 (electronic)
  • Publisher: Duke University Press
  • Discipline(s): Mathematics
  • Full text available in Euclid: 1935--
  • Access: By subscription only
  • Euclid URL: http://projecteuclid.org/dmj

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MR Citation Database MCQ (2016): 2.23
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Eigenfactor: Duke Mathematical Journal
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Featured article

Geometry of pseudodifferential algebra bundles and Fourier integral operators

Varghese Mathai and Richard B. Melrose Volume 166, Number 10 (2017)
Abstract

We study the geometry and topology of (filtered) algebra bundles ΨZ over a smooth manifold X with typical fiber ΨZ(Z;V), the algebra of classical pseudodifferential operators acting on smooth sections of a vector bundle V over the compact manifold Z and of integral order. First, a theorem of Duistermaat and Singer is generalized to the assertion that the group of projective invertible Fourier integral operators PG(FC(Z;V)) is precisely the automorphism group of the filtered algebra of pseudodifferential operators. We replace some of the arguments in their work by microlocal ones, thereby removing the topological assumption. We define a natural class of connections and B-fields on the principal bundle to which ΨZ is associated and obtain a de Rham representative of the Dixmier–Douady class in terms of the outer derivation on the Lie algebra and the residue trace of Guillemin and Wodzicki. The resulting formula only depends on the formal symbol algebra ΨZ/Ψ. Examples of pseudodifferential algebra bundles are given that are not associated to a finite-dimensional fiber bundle over X.