Solvability of left invariant differential operators on certain solvable Lie groups
In this work, the authors uses non-commutative harmonic analysis in the study of differential operators on a certain class of solvable Lie groups. A left-invariant differential operator (a differential operator that commutes with left translations on the group) can be synthesized in terms of differential operators on lower-dimensional spaces. This synthesis is easily described for a certain class of simply connected solvable Lie groups, those arising as semi-direct products of simply connected abelian groups. We derive sufficient conditions for the global solvability of left invariant differential operators on such groups in terms of the lower-dimensional differential operators. These conditions are seen to be satisfied for certain classes of second-order differential operators, thus yielding global solvability. Specifically elliptic, sub-elliptic, transversally elliptic and parabolic operators are investigated.
- Research Organization:
- Colorado Univ., Boulder (USA)
- OSTI ID:
- 6984741
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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