On \(p\)-adic Green's functions
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 \({p^{\alpha+ 2}(p^\alpha- 1)\over p^{\alpha+ 2}- 1} \lambda^{- 2}\).
scientific article; zbMATH DE number 589592