From several results in recent years, starting with Hörmander’s characterization of the constant coefficient partial differential equations P (D)u = f that have a real analytic solution u for every real analytic function f , it has become clear that certain properties of the partial differential operator P (D) are equivalent to estimates of Phragmén–Lindelöf type for plurisubharmonic functions ...

We investigate a version of the Phragmén–Lindelöf theorem for solutions of the equation ∆∞u = 0 in unbounded convex domains. The method of proof is to consider this infinity harmonic equation as the limit of the p-harmonic equation when p tends to ∞.

We investigate whether an arbitrary base for a topological space can be partitioned into two bases. We prove that every base for a T3 Lindelöf topology can be partitioned into two bases while there exists a consistent example of a rst countable, 0-dimensional, Hausdor space of size and weight ω1 which admits a base without a partition to two bases.

Topological groups whose underlying spaces are basically disconnected, F-, or F′-spaces but not P-spaces considered. It is proved, in particular, that the existence of a Lindelöf disconnected topological group which P-space equivalent to Boolean countable pseudocharacter, free and Abelian zero-dimensional non-P-spaces never F′-spaces, F′-group selective ultrafilters on ω.

The remainder $$E_\Gamma (X)$$ in the Prime Geodesic Theorem for Picard group $$\Gamma = \mathrm {PSL}(2,\mathbb {Z}[i])$$ is known to be bounded by $$O(X^{3/2+\epsilon })$$ under assumption of Lindelöf hypothesis quadratic Dirichlet L-functions over Gaussian integers. By studying second moment , we show that on average same bound holds unconditionally.

We characterize lower growth estimates for subsolutions in halfspaces of fully nonlinear partial differential equations on the formF(x,u,Du,D2u)=0 terms solutions to ordinary built upon assumptions F. Using this characterization we derive several sharp Phragmen–Lindelöf-type theorems certain classes well known PDEs. The equation need not be uniformly elliptic nor homogeneous and obtain results ...