Zeros of orthogonal Laurent polynomials and solutions of strong Stieltjes moment problems

✍ Scribed by C. Bonan-Hamada; W.B. Jones; O. Njåstad

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 241 KB
• Volume: 235
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2010.06.015

✦ Synopsis

The strong Stieltjes moment problem for a bisequence {c n } ∞ n=-∞ consists of finding positive

Orthogonal Laurent polynomials associated with the problem play a central role in the study of solutions. When the problem is indeterminate, the odd and even sequences of orthogonal Laurent polynomials suitably normalized converge in C \ {0} to distinct holomorphic functions. The zeros of each of these functions constitute (together with the origin) the support of two solutions µ (∞) and µ (0) . We discuss how odd and even subsequences of zeros of the orthogonal Laurent polynomials converge to the support points of µ (∞) and µ (0) .