Asymptotical behavior of one class of p-adic singular Fourier integrals

Abstract: We study the asymptotical behavior of the p-adic singular Fourier integrals where is a quasi associated homogeneous distribution (generalized function) of degree and order m, , , and are a multiplicative, a normed multiplicative, and an additive characters of the field of p-adic numbers, respectively, is a test function, , . If 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. [Copyright &y& Elsevier]