Amazon.com description: Product Description: This volume looks at the spectral theory of global hypoelliptic pseudodifferential operators in Rn and the asymptotic estimate of the eigenvalue distribution function N of a hypoelliptic differential operator with polynomial coefficients in Rn. The first section introduces the pseudodifferential calculus with respect to a multi-quasi-elliptic weight; while the second part computes the asymptotic expansion of N for a multi-quasi-elliptic differential operator with polynomial coefficients. This is achieved by computing the asymptotic expansion of the Weyl term V. In this way, results are obtained with respect to a refinement of the asymptotic formula and the class of symbols considered.