Suppose you have a reasonable continuous function on some interval, say on , and you want to approximate it by a trigonometric polynomial. A straightforward approach is to write… 184 more words
Tags » Trigonometric Polynomials
1. The set of squares does not contain arbitrarily long arithmetic progressions.
As we have mentioned in the beginning of this discussion, Rudin was originally interested (among other things) in the number of terms the set of squares has in arithmetic progressions. 529 more words
This is the first of a series of posts concerning the Rudin-Hardy-Littlewood Conjecture. To give a taste of the problem right away let us consider to be a trigonometric polynomial of the form… 1,277 more words