On the convergence rate ofs-numbers of compact Hankel operators

It is well known that the sequence ofs-numbers {s_n},n=0, 1,..., of a compact operator, and particularly a compact Hankel operator =[h_j+k–1], converges monotonically to zero. Since the (n + 1)sts-number s_n measures the error ofL(¦z¦=1) approximation, modulo an additive H function, by nth degree proper rational functions whose poles are restricted to ¦z¦ < 1, it is very important to study how fast {s_n} converges to zero. It is not difficult to see that ifh_n=O(n^–), for some > 1, thens_n=O(n^–). In this paper we construct, for any given sequence_n 0, a compact Hankel operator such thats_nn for alln.The research of C. K. Chui was supported by the SDIO/IST managed by the U.S. Army under Contract No. DAAL-03-87-K-0025, and by the NSF under Grant No. DMS-8901345. X. Li's research was supported by the SDIO/IST managed by the U.S. Army under Contract No. DAAL-03-87-K-0025. The research of J. D. Ward was supported by the NSF under Grant No. DMS-8901345.