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Analysis Mathematica

, Volume 43, Issue 4, pp 603–627 | Cite as

Noncommutative potential theory

  • L. LempertEmail author
Article
  • 48 Downloads

Abstract

We propose to view hermitian metrics on trivial holomorphic vector bundles E → Ω as noncommutative analogs of functions defined on the base Ω, and curvature as the notion corresponding to the Laplace operator or ∂∂̅. We discuss noncommutative generalizations of basic results of ordinary potential theory, mean value properties, maximum principle, Harnack inequality, and the solvability of Dirichlet problems.

Keywords

curvature of hermitian metrics maximum principle mean value property Dirichlet problem 

Mathematics Subject Classification

31C05 31C10 47A56 47A68 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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