Spectral properties of pseudo-differential operators over the compact group of p-adic integers and compact Vilenkin groups

2019/12/24 by Juan Pablo Velasquez-Rodriguez, Velasquez-Rodriguez, Juan Pablo
Mathematics · #advanced mathematical theories #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1912.11407

Abstract

In this paper. we study properties such as L^r-boundedness, compactness, belonging to Schatten classes and nuclearity, Riesz spectral theory, Fredholmness, ellipticity and Gohberg's lemma, among others, for pseudo-differential operators over the compact group of p-adic integers ℤ_p^d, where the author in a recent paper introduced a notion of Hörmander classes and pseudo-differential calculus. We extend the results to compact Vilenkin groups which are essentially the same as ℤ_p^d. Also, we provide a new definition of Hörmander classes for pseudo-differential operators acting on non-compact Vilenkin groups and an explicit formula for the Fredholm spectrum in terms of the associated symbol.

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