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

#### Peanut allergy and Polar interpolation

Draw a closed curve passing through the points and : more specifically, from (3,0) to (0,1) to (-3,0) to (0,-1) and back to (3,0).

I’ll wait. 478 more words

#### Why Do We Like Polynomials?

Polynomials turn up all over the place. There are multiple good reasons for this. For one, suppose we have any continuous function that we want to study. 583 more words

#### The Rudin (Hardy-Littlewood) Conjecture, Notes 3: Omissions.

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

#### The Rudin (Hardy-Littlewood) Conjecture, Notes 2: A closer look at Λ(p)-sets.

This is the second post on Rudin’s conjecture. For the first introductory notes see here. In this post I will try to build some more intuition on -sets by studying some examples and discussing their properties. 1,711 more words

#### The Rudin (Hardy-Littlewood) Conjecture, Notes 1: Introduction and basic facts.

**1. Introduction. **

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