
fourier transforms

Okay what is the definition of "even Schwartz function"? Are the given functions even Schwarz functions?

A Schwartz function is a "rapidly decaying" function, in the sense that the function and all its derivatives decay faster than $\displaystyle \frac{1}{x^n}$ for n = 1,2,3,4,...
Schwartz space  Wikipedia, the free encyclopedia
Those functions are certainly even, but none of them is Schwartz... the first two only decay as fast as $\displaystyle \frac{1}{y^a}$, and the last decays much slower than that (as $\displaystyle \frac{1}{logy}$). So, the Schwartz thing isn't useful here.