Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$\mathbb K$ is a $\textit{local field}$ if it is any totally disconnected, locally compact, non-discrete, complete field.For examples: $\mathbb Q_p$, any finite extension of $\mathbb Q_p$, field of Laurent series on finite field. For each $\gamma\in\mathbb Z$, we denote $B_{\gamma}=\{x\in\mathbb K: \; |x|\leq q^\gamma\}$, the usual balls.

Let $f$ be any function in $L^2(\mathbb K)$ and $\chi_\gamma$ is the chareteristic function of $B_\gamma$. It is obvious that $f_\gamma=f\cdot \chi_\gamma$ converges pointwise to $f$ and $f_\gamma\to f$ in $L^2$ when $\gamma\to-\infty$. Is it true that their Fourier transform $Ff_n$ also converges pointwise almost everywhere to $Ff$

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.