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Hörmander Classes of Pseudo-Differential Operators over the Compact Group of p-Adic Integers

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Abstract

The purpose of this paper is to introduce new definitions of Hörmander classes for pseudo-differential operators over the compact group of p-adic integers. Our definitions possesses a symbolic calculus, asymptotic expansions and parametrices, together with an interesting relation with the infinite matrices algebras studied by K. Gröchenig and S. Jaffard. Also, we show how our definition of Hörmander classes is related to the definition given in the toroidal case by M. Ruzhansky and V. Turunen. In order to show the special properties of our definition, in a later work, we will study several spectral properties in terms of the symbol for pseudo-differential operators in the Hörmander classes here defined.

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Acknowledgments

The author thanks Professor Michael Ruzhansky for his help during the development of this work.

Funding

The author was supported by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations.

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Authors and Affiliations

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

    J. P. Velasquez-Rodriguez

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Correspondence to J. P. Velasquez-Rodriguez.

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Velasquez-Rodriguez, J.P. Hörmander Classes of Pseudo-Differential Operators over the Compact Group of p-Adic Integers. P-Adic Num Ultrametr Anal Appl 12, 134–162 (2020). https://doi.org/10.1134/S2070046620020053

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  • DOI: https://doi.org/10.1134/S2070046620020053

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