The reproducing Kernel of the Sobolev space on an interval.

Let H^n(a,b) be the one-dimensional Sobolev Hilbert space of order n on the interval (a,b) (n=1,2,\dots). The explicit form of the reproducing kernel of H^n(a,b) on finite interval was already known in the case for n=1,2,3. In this paper we obtain the explicit form of the reproducing kernel of H^n(a,b) on any interval for general n. [ABSTRACT FROM AUTHOR]