I want to prove the following inequality:
$$\sum\limits_{k\in\mathbb{N}}\Big(\int \big|f(x)\big|\big|g(x-k)\big|dx\Big)^2 \leq \big\|f\big\|^2 \sum\limits_{k\in\mathbb{N}}\Big (\int\big|g(x-k)\big|dx\Big)^2$$
where
$$\|f\|^2=\int |f(x)|^2dx.$$
My attempt: Just prove the following inequality...
I am reading an article[1] that states:
Let k be a fixed local field. Then there is an integer q=pr, where p is a fixed prime element of k and r is a positive integer, and a norm |.| on k such that for all x∈k we have |x|≥0 and for each x∈k\{0} we get |x|=qm for some integer m. This norm is...
I am looking for a local field of positive characteristic, like Q22 was used in this article:
http://8pic.ir/images/s9oiiuqqkq989w3posu9.png
in fact, i need an another Example of a local field of positive characteristic like Q22 .