On \(p\)-adic Green's functions
type: Item
instance of: scholarly article
title: On \(p\)-adic Green's functions
zbMATH Open document ID: 0843.35147
DOI: 10.1007/BF01074114
published in: Theoretical and Mathematical Physics
publication date: 1994-07-13T00:00:00Z
review text: A class of pseudodifferential operators over a \(p\)-adic local field is considered, for which the resolvent is an integral operator with a nonnegative kernel (the Green function). A typical example is the operator with the symbol \(|h(\xi_1,\dots, \xi_n)|^\alpha_p\), \(\xi_1,\dots, \xi_n\in \mathbb{Q}_p\), where \(\alpha> 0\), \(h\) is a quadratic form over \(\mathbb{Q}_p\) which does not represent zero (this is possible only for \(n\leq 4\)). The asymptotics of the Green function has been calculated for \(n= 2\) and \(n= 4\). The asymptotic formula for the latter case contains a misprint -- the coefficient should read \({p^{\alpha+ 2}(p^\alpha- 1)\over p^{\alpha+ 2}- 1} \lambda^{- 2}\).
Mathematics Subject Classification ID: 35S99
Mathematics Subject Classification ID: 81Q99
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 47S10
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 589592
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: \(p\)-adic local field
zbMATH Keywords: resolvent
zbMATH Keywords: Green function
zbMATH Keywords: asymptotics
author: Anatoly N. Kochubei
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
cites work: Q5532660
cites work: Q5566639
cites work: Special functions on locally compact fields
cites work: p-adic quantum mechanics
cites work: Q5670687
cites work: Q3961610
cites work: Q4138813
cites work: Q4402415
full work available at URL: https://doi.org/10.1007/bf01074114
OpenAlex ID: W2000873533
description: scientific article; zbMATH DE number 589592