fourier transforms

Fact: every even Schwartz function on http://alt1.artofproblemsolving.com/...3eaea88a57.gif is the fourier transform of some integrable function.

Using (or not!) that fact, find out if the following are the Fourier transforms of some integrable functions on R:

A. http://alt2.artofproblemsolving.com/...ba6357f194.gif, with http://alt1.artofproblemsolving.com/...315731cd44.gif

B. http://alt2.artofproblemsolving.com/...2de0e68eee.gif, with http://alt1.artofproblemsolving.com/...81f28a3a97.gif

C. http://alt1.artofproblemsolving.com/...2bbdc112e0.gif

i appreciate ur time.

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 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 , and the last decays much slower than that (as ). So, the Schwartz thing isn't useful here.