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Acta Applicandae Mathematica

, Volume 80, Issue 2, pp 123–174 | Cite as

Pseudo-Differential Operators in Algebras of Generalized Functions and Global Hypoellipticity

  • Claudia Garetto
Article

Abstract

The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity for the corresponding pseudo-differential equations. This calculus and this frame are proposed as tools for the study in Colombeau algebras of partial differential equations globally defined on R n .

Colombeau algebras pseudo-differential operators global hypoellipticity 

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© Kluwer Academic Publishers 2004

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  • Claudia Garetto

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