Uniqueness theorems for weighted harmonic functions in the upper half-plane

• Published in: Journal d'analyse mathématique (Jerusalem) Vol. 152; no. 1; pp. 317 - 359
• Main Authors: Olofsson, Anders, Wittsten, Jens
• Format: Journal Article
• Language: English
• Published: Jerusalem The Hebrew University Magnes Press 01.04.2024; Springer Nature B.V
• Subjects: Abstract Harmonic Analysis; Analysis; Dirichlet problem; Dynamical Systems and Ergodic Theory; Functional Analysis; Geodesy; Half planes; Harmonic functions; Infinity; Matematik; Matematisk analys; Mathematical Analysis; Mathematical Sciences; Mathematics; Mathematics and Statistics; Natural Sciences; Naturvetenskap; Partial Differential Equations; Polynomials; Uniqueness theorems

We consider a class of weighted harmonic functions in the open upper half-plane known as α -harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the real line and an appropriate vanishing condition at infinity. We...