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

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

2008-08-25

arxiv.org/abs/0808.3252v1

Physics

Mathematical Physics

Scientific paper

We study the asymptotical behavior of the $p$-adic singular Fourier integrals $$ J_{\pi_{\alpha},m;\phi}(t) =\bigl< f_{\pi_{\alpha};m}(x)\chi_p(xt), \phi(x)\bigr> =F\big[f_{\pi_{\alpha};m}\phi\big](t), \quad |t|_p \to \infty, \quad t\in \bQ_p, $$ where $f_{\pi_{\alpha};m}\in {\cD}'(\bQ_p)$ is a {\em quasi associated homogeneous} distribution (generalized function) of degree $\pi_{\alpha}(x)=|x|_p^{\alpha-1}\pi_1(x)$ and order $m$, $\pi_{\alpha}(x)$, $\pi_1(x)$, and $\chi_p(x)$ are a multiplicative, a normed multiplicative, and an additive characters of the field $\bQ_p$ of $p$-adic numbers, respectively, $\phi \in {\cD}(\bQ_p)$ is a test function, $m=0,1,2...$, $\alpha\in \bC$. If $Re\alpha>0$ the constructed asymptotics constitute a $p$-adic version of the well known Erd\'elyi 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.

Affiliated with

Also associated with

No associations

Rating

Asymptotical behavior of one class of $p$-adic singular Fourier integrals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotical behavior of one class of $p$-adic singular Fourier integrals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotical behavior of one class of $p$-adic singular Fourier integrals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-380141