THE EXPLICIT FORMULAS FOR REPRODUCING KERNEL OF SOME HILBERT SPACES.

This paper is devoted to finding explicit formulas for two kinds of reproducing kernels in some reproducing kernel spaces. Usually for calculating the reproducing kernel of space Wm2 [a;b], one must solve a large system of ordinary differential equations with 4m equations in 4m unknowns. Hence, it is worthy to have explicit formulas to save time and computational efforts. The advantage of using these formulas is clearly seen in the plotted graphs. [ABSTRACT FROM AUTHOR]