Ellipticity refers to a property of certain differential operators, specifically indicating that the operator behaves well with respect to solutions of differential equations. In the context of noncommutative geometry, ellipticity is crucial for the analysis of Dirac operators, as it ensures that these operators possess desirable analytical properties, like having a well-defined kernel and a regular spectrum. This concept is fundamental when examining the geometric structures of noncommutative spaces and their implications for physics and mathematics.
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