A class of globally analytic hypoelliptic operators on compact Lie groupsOberseminar Global Analysis and Operator Algebras

by Max Reinhold Jahnke (Universität zu Köln)

Tuesday Jan 21, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Seminarraum 0.008 (Mathezentrum)

In this talk, I will discuss global analytic hypoellipticity for a class of differential operators that can be expressed as $P=\sum _{j=1}^{\nu }{X}_j^2+X_0+a$ with real-analytic coefficients on compact Lie groups. To obtain global analytic hypoellipticity, we assume that the vector fields satisfy Hörmander's finite type condition and that there exists a closed subgroup whose action leaves the vector fields invariant. We further assume the operator is elliptic in directions transversal to the action of the subgroup. This paves the way for further studies on the regularity of sums of squares on principal fiber bundles.