Characterization of global Phragmén–Lindelöf conditions for algebraic varieties by limit varieties only
Volume 88 / 2006
Annales Polonici Mathematici 88 (2006), 83-95 MSC: Primary 32U05; Secondary 31C10, 32C25. DOI: 10.4064/ap88-1-6
For algebraic surfaces, several global Phragmén–Lindelöf conditions are characterized in terms of conditions on their limit varieties. This shows that the hyperbolicity conditions that appeared in earlier geometric characterizations are redundant. The result is applied to the problem of existence of a continuous linear right inverse for constant coefficient partial differential operators in three variables in Beurling classes of ultradifferentiable functions.