2008/08/25 by A. Yu. Khrennikov, Khrennikov, A. Yu., V. M. Shelkovich +1
Mathematics · #11E95 #34E05 (Primary) 76M45 #46F12 (Secondary) #FOS: Mathematics #FOS: Physical sciences #General Mathematics (math.GM) #Mathematical Physics (math-ph) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.0808.3252
openalex publication_date 2008/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the asymptotical behavior of the p-adic singular Fourier integrals Jπα,m;ϕ(t) =\bigllt; fπα;m(x)χp(xt), ϕ(x)\bigrgt; =F[fπα;mϕ](t), |t|p → ∞, t∈ \bQp, where fπα;m∈ \cD'(\bQp) is a \em quasi associated homogeneous distribution (generalized function) of degree πα(x)=|x|pα-1π1(x) and order m, πα(x), π1(x), and χp(x) are a multiplicative, a normed multiplicative, and an additive characters of the field \bQp of p-adic numbers, respectively, ϕ∈ \cD(\bQp) is a test function, m=0,1,2..., α∈ \bC. If Reα>0 the constructed asymptotics constitute a p-adic version of the well known Erdélyi lemma. Theorems which give asymptotic expansions of singular Fourier integrals are the Abelian type theorems. In contrast to the real case, all constructed asymptotics have the \it stabilization property.