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Pseudo-differential Operators Associated to General Type I Locally Compact Groups

  • Marius MăntoiuEmail author
  • Maximiliano Sandoval
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)

Abstract

In a recent paper by M. Măntoiu and M. Ruzhansky, a global pseudo-differential calculus has been developed for unimodular groups of type I. In the present article we generalize the main results to arbitrary locally compact groups of type I. Our methods involve the use of Plancherel’s theorem for non-unimodular groups. We also make connections with a \(C^*\)-algebraic formalism, involving dynamical systems, and give explicit constructions for the group of affine transformations of the real line.

Keywords

Locally compact group Lie group Noncommutative Plancherel theorem Modular function Pseudo-differential operator 

Notes

Acknowledgement

M. Sandoval has been supported by Beca de Magister Nacional 2016 Conicyt and partially supported by Núcleo Milenio de Física Matemática RC120002. M. Măntoiu is supported by the Fondecyt Project 1160359.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Name, Facultad de Ciencias, Departamento de MatematicasUniversidad de ChileSantiagoChile
  2. 2.Facultad de CienciasUniversidad de ChileSantiagoChile

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