Abstract
In this paper we develop a theory of parabolic pseudodifferential operators in anisotropic spaces. We construct a symbolic calculus for a class of symbols globally defined on ℝ n+1×ℝ n+1, and then develop a periodisation procedure for the calculus of symbols on the cylinder $$\mathbb{T}^n $$ ×ℝ. We show Garding's inequality for suitable operators and precise estimates for the essential norm in anisotropic Sobolev spaces. These new mapping properties are needed in localization arguments for the analysis of numerical approximation methods.
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