Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

we have that the function (for suitable f)

$ F(x)= \sum_{-\infty}^{\infty}f(x+n) $ is INVARIANT under any integer traslation

$ y=x+n$ for integer 'n'

however my question is can we find a lattice which is invariant under DILATIONS i mean under the transformation $ y=qx$ for integer (positive) or rational 'q' ??

so i am looking a formula like $ F(x)= \sum f(qx) $ so F(x) is invariant under transformation of the form $ y=qx$ thanks.

share|improve this question
2  
What do you mean by a "lattice"? Exactly what are you looking for? A function? What should be the domain of the function? –  Seva Mar 31 '12 at 9:53
    
$F(x) = \sum_{n=-\infty}^\infty f(q^n x)$ ? –  Noam D. Elkies Mar 31 '12 at 18:52
add comment

1 Answer 1

up vote 1 down vote accepted

If you lattice $X$ contains at least a point $x$ it must contains all points $qx$ with $q$ rational. Hence $X$ is a dense set. As a consequence if your function $f$ is positive in some interval then function $F$ is infinite everywhere.

share|improve this answer
add comment

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.