Two applications of the subnormality of the Hessenberg matrix related to general orthogonal polynomials

✍ Scribed by V. Tomeo; E. Torrano

• Book ID: 104039497
• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 202 KB
• Volume: 435
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2011.04.027

✦ Synopsis

In this paper we prove two consequences of the subnormal character of the Hessenberg matrix D when the hermitian matrix M of an inner product is a moment matrix. If this inner product is defined by a measure supported on an algebraic curve in the complex plane, then D satisfies the equation of the curve in a noncommutative sense. We also prove an extension of the Krein theorem for discrete measures on the complex plane based on properties of subnormal operators.