Orthogonal Polynomials Associated with Equilibrium Measures on R

Let K be a non-polar compact subset of R and mu K denote the equilibrium measure of K. Furthermore, let P-n ( therefore mu K) be the n-th monic orthogonal polynomial for mu K. It is shown that parallel to P-n ( therefore mu K) parallel to L-( mu K)(2), the Hilbert norm of P-n (therefore mu K) in L-2(mu K), is bounded below by Cap(K)(n) for each n is an element of N. A sufficient condition is given for (parallel to P-n (therefore mu K) parallel to(L2)(mu K)/Cap(K) (n))(infinity)(n=1) to be unbounded. More detailed results are presented for sets which are union of finitely many intervals.