2 5 A ug 2 00 8 Asymptotical behavior of one class of p - adic singular Fourier integrals
نویسندگان
چکیده
We study the asymptotical behavior of the p-adic singular Fourier integrals Jπα,m;φ(t) = 〈 fπα;m(x)χp(xt), φ(x) 〉 = F [ fπα;mφ ] (t), |t|p → ∞, t ∈ Qp, where fπα;m ∈ D ′(Qp) is a quasi associated homogeneous distribution (generalized function) of degree πα(x) = |x| α−1 p π1(x) and orderm, πα(x), π1(x), and χp(x) are a multiplicative, a normed multiplicative, and an additive characters of the field Qp of p-adic numbers, respectively, φ ∈ D(Qp) is a test function, m = 0, 1, 2 . . . , α ∈ C. 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 stabilization property.
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