Geometric interpretation of the Phragmén-Lindelöf estimates (Q1284425)

In Section 1 local hyperbolicity of analytic functions is discussed, while Section 2 gives sufficient conditions for Phragmén-Lindelöf implications to hold on zero-sets of such functions. Section 3 states a geometric version of Hörmander's criterion for global existence on open convex domains in \(\mathbb{R}^n\) of real analytic solutions to linear partial differential equations with constant coefficients. A new example explains in what sense the method of the author, using accurate Phragmén-Lindelöf estimates, is sharper than the others which have appeared in the literature.