What does a hat or star means in math?

What are the general uses of the hat and star symbol in math? Or could you please point me to a page that discusses this? Thanks.

Solution 1:

There is a nice list for $*$ in this article

I guess another (more general) term for "hat" is Circumflex

Solution 2:

Different branches of mathematics may have varying conventional usages of these kind of "decorations". Typically they denote a transformed version of the base variable (e.g. $\hat{f}$ denoting the Fourier transform of $f$ as mentioned in another answer). Or, they may denote a special or specific value of a variable ($x^*$ giving the value of $x$ minimizing $f$ from another answer.) The $*$ symbol is often used for arbitrary associative binary operations. Etc. etc.