Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, and specifically the field of partial differential equations (PDEs), a parametrix is a generalization of the notion of a fundamental solution of a PDE. A fundamental solution for a differential operator P(D) with constant coefficients is a distribution u on Rn such that. where is some C function with compact support. The parametrix is a useful concept in the study of elliptic differential operators and, more generally, of hypoelliptic pseudodifferential operators, since for such operators over appropriate domains a parametrix can be shown to exist, and be a smooth function away from the origin.More generally, if L is any pseudodifferential operator, then another pseudodifferential operator L+ is called a parametrix for L if the operators

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