A form of classical Liouville theorem for polyharmonic functions
type: Item
instance of: scholarly article
title: A form of classical Liouville theorem for polyharmonic functions
zbMATH Open document ID: 0965.31006
author: Mitsuru Nakai
author: Toshimasa Tada
published in: Hiroshima Mathematical Journal
publication date: 2001-05-13T00:00:00Z
review text: The authors prove the following version of Liouville's theorem for polyharmonic functions: If \(m\) is a positive integer and \(s\) is any real number with \(s>2m-2\), then \(u\), a polyharmonic function of order \(m\) is a polyharmonic polynomial of degree less than \(s\) if and only if there exists an increasing divergent sequence \(\left( r_i\right) _{i\geq 1}\) of positive numbers such that \[ \lim \inf _{i\rightarrow \infty }\left( \min _{\left|x\right|=r_i}\frac{ u\left( x\right) }{\left|x\right|^s}\right) \geq 0 . \]
Mathematics Subject Classification ID: 31B30
zbMATH DE Number: 1539261
zbMATH Keywords: Liouville theorem
zbMATH Keywords: spherical harmonics
zbMATH Keywords: Fourier expansion
reviewed by: Adrian Carabineanu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206124683
OpenAlex ID: W2139410122
Wikidata QID: Q128898750
DOI: 10.32917/HMJ/1206124683
description: scientific article; zbMATH DE number 1539261