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Journal d'Analyse Mathématique

, Volume 135, Issue 2, pp 757–800 | Cite as

Fourier multipliers, symbols, and nuclearity on compact manifolds

  • Julio Delgado
  • Michael RuzhanskyEmail author
Open Access
Article

Abstract

The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite-dimensional subspaces. As a consequence, given a compact manifold M endowed with a positive measure, we introduce a notion of the operator’s full symbol adapted to the Fourier analysis relative to a fixed elliptic operator E. We give a description of Fourier multipliers, or of operators invariant relative to E. We apply these concepts to study Schatten classes of operators on L2(M) and to obtain a formula for the trace of trace class operators. We also apply it to provide conditions for operators between Lp-spaces to be r-nuclear in the sense of Grothendieck.

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Copyright information

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Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUnited Kingdom

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