Paolo Boggiatto | Akateeminen Kirjakauppa

This book concerns the spectral theory of global hypoelliptic pseudodifferential operators in Rn and the asymptotic estimate of the eigenvalue distribution function N(l) of a hypoelliptic differential operator with polynomial coefficients in Rn. In the first part of the book the pseudodifferential calculus with respect to a multi-quasi-elliptic weight is introduced. In particular, the self-adjoint property is related to the Weyl symbol, while positivity, continuity and compactness in L2(Rn) are investigated by the Anti-Wick symbol. In the second part, after an introduction to the spectral theory for global hypoelliptic essentially selfadjoint operators, the asymptotic expansion of N(l) is computed for a multi-quasi-elliptic differential operator with polynomial coefficients. In particular, this is achieved by computing the asymptotic expansion of the Weyl term V(l). In this way some original results are obtained both with respect to a refinement of the asymptotic formula and the class of symbols considered.