A Phragmén-Lindelöf theorem for function algebras

The algebraic surfaces on which the classical Phragmén - Lindelöf theorem holds

Let V be an algebraic variety in Cn . We say that V satisfies the strong Phragmén-Lindelöf property (SPL) or that the classical Phragmén-Lindelöf Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by |z| + o(|z|) on V and by 0 on the real points in V already is bounded by A| Im z|. For algebraic ...

INFINITELY MANY ZEROS OF ζ ( s ) LIE ON

ζ(0 + it) = O(|t| 1 2 + ), for each > 0. Apply the Phragmén–Lindelöf Theorem to ζ(s) in a small interval containing 1. Clearly, we can make the linear function arising from the Phragmén–Lindelöf Theorem to pass arbitrarily close to 0 at σ = 1. Thus, as |t| → ∞, ζ(1 + it) = O(|t| ), for each > 0. To apply the Phragmén–Lindelöf Theorem to ζ(s) in the strip 0 ≤ σ ≤ 1, we set k(σ) = aσ + b. Thus, k...

A Strong Maximum Modulus Theorem for Maximal Function Algebras

phragmén-lindelöf type results for a class of nonlinear damped wave equations

this paper deals with the behavior at infinity of solutions to a class of wave equations with nonlinear dampingterms defined in a semi-infinite cylinder. the spatial behavior of solutions is studied and an alternative ofphragmén-lindelöf type theorems is obtained in the results. the main point in the contribution is the use of energy method.

A Representation Theorem for Co-diagonalizable Algebras

This abstract is a summary of a lecture given at the Seminar of the Department of Logic and Methodology of Sciences, Wroc law University, 23 May 1985. The present work refers directly to the investigations of Buszkowski and Prucnal [1] and that of Esakia [2], generalizing their results. Our main representation theorem for co-diagonalizable algebras (Theorem 2) is obtained by application of cert...