Here we study univariate density estimation based on the theory of reproducing kernel Hilbert space. Our density estimator is 
constructed by minimizing L_2 distance between the estimated density and the unknown true density. Compared to the methods 
of smoothing splines, the proposed approach is mathematically simple and computationally efficient.  

We also show that in function spaces of very smooth functions, such as the infinite-order Sobolev spaces, the method yields a rate 
of O(log n/n) of convergence. Simulations are performed to study the finite sample properties of the estimator.