Memoirs of the American Mathematical Society 1998; 92 pp; softcover Volume: 134 ISBN10: 0821807846 ISBN13: 9780821807842 List Price: US$48 Individual Members: US$28.80 Institutional Members: US$38.40 Order Code: MEMO/134/636
 This work studies the failure of analytichypoellipticity (AH) of two partial differential operators. The operators studied are sums of squares of real analytic vector fields and satisfy Hormander's condition; a condition on the rank of the Lie algebra generated by the brackets of the vector fields. These operators are necessarily \(C^\infty\)hypoelliptic. By reducing to an ordinary differential operator, the author shows the existence of nonlinear eigenvalues, which is used to disprove analytichypoellipticity of the original operators. Readership Research mathematicians interested in smoothness/regularity of solutions of PDE. Table of Contents  Statement of the problems and results
 Sums of squares of vector fields on \(\mathbb R^3\)
 Sums of squares of vector fields on \(\mathbb R^5\)
 Bibliography
