Regularity of class of differential operators

2012/06/15 by Ernesto Buzano, Alessandro Oliaro, Buzano, Ernesto +1
Mathematics · #35H99 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35H99

paper · pdf · doi:10.48550/arxiv.1206.3455

9 pages

arxiv created 2012/06/15 · arxiv updated 2012/06/18

Abstract

In this paper we deal with the problem of regularity for non hypo-elliptic partial differential equations with polynomial coefficients. An operator A on on the space of tempered distributions S^′ is regular if u belongs to the Schwartz class \mathcal S whenever Au∈ \mathcal S. By using tensor products of topological vector spaces and a kind of Wigner transform we reduce the study of regularity of a non hypo-elliptic differential operator, like the twisted laplacian, to a hypo-elliptic one, like the harmonic oscillator.

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