Analytic Hypoellipticity for Generalized Baouendi-Goulaouic Operators

This work studies the analytic regularity of solutions to certain second-order equations defined by a sum of squares of vector fields. It describes a method for constructing singular solutions to generalized Baouendi-Goulaouic-type operators. This construction is quite explicit and it involves the study of the first eigenvalue and the first eigenfunction of a generalized harmonic oscillator with potential depending on a large parameter.