ABSTRACT

IJ«,) - Jml "'I lt\x)lie-'''·'•' - ,-'""1 dx and )e-·<~.~kl -e-;~,x.~)......,. 0 as~-~. we conclude that}(~k)- j(~) by Lebesgue's convergence theorem. Thus J is a bounded continuous function on Rn. From the Riemann~Lebesgue lemma [41, it follows that)(~)- 0 as )t) - ®. But in general j may not be integrable, as may be seen by taking the Fourier transfonn of the function in R which equals I on the open interval (0, I) and 0 otherwise. A simple calculation gives the result as 2 sin t/t. which is not in L 1.