A non-parametric estimate of a probability density function

Non-parametric estimate (2) of multivariate density is proposed. The estimate is obtained by the inverse Fourier transformation of the empirical distribution characteristic function. Our estimate is similar to that of Murthy [1], but in our case the $p$-dimentional window is not absolutely integrable. We prove that our estimate is consistent, asymptotically unbiased and asymptotically normal.