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Analysis and Partial Differential Equations: Perspectives from Developing Countries pp 172–190Cite as

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

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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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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Authors and Affiliations

  1. Name, Facultad de Ciencias, Departamento de Matematicas, Universidad de Chile, Las Palmeras 3645, Santiago, Chile

    Marius Măntoiu

  2. Facultad de Ciencias, Universidad de Chile, Las Palmeras 3645, Santiago, Chile

    Maximiliano Sandoval

Authors
  1. Marius Măntoiu
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  2. Maximiliano Sandoval
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Corresponding author

Correspondence to Marius Măntoiu .

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Editors and Affiliations

  1. School of Mathematical Sciences, Queen Mary University of London, London, UK

    Julio Delgado

  2. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Michael Ruzhansky

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Măntoiu, M., Sandoval, M. (2019). Pseudo-differential Operators Associated to General Type I Locally Compact Groups. In: Delgado, J., Ruzhansky, M. (eds) Analysis and Partial Differential Equations: Perspectives from Developing Countries. Springer Proceedings in Mathematics & Statistics, vol 275. Springer, Cham. https://doi.org/10.1007/978-3-030-05657-5_11

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