✍ Scribed by A. Bultheel; P. González-Vera; E. Hendriksen; O. Njåstad
No coin nor oath required. For personal study only.
In Akhiezer's book [``The Classical Moment Problem and Some Related Questions in Analysis, '' Oliver 6 Boyd, EdinburghÂLondon, 1965] the uniqueness of the solution of the Hamburger moment problem, if a solution exists, is related to a theory of nested disks in the complex plane. The purpose of the present paper is to develop a similar nested disk theory for a moment problem that arises in the study of certain orthogonal rational functions. Let [: n ] n=0 be a sequence in the open unit disk in the complex plane, let B 0 =1 and B n (z)= ǹ k=0 : k
📜 SIMILAR VOLUMES
When one wants to use Orthogonal Rational Functions (ORFs) in system identification or control theory, it is important to be able to avoid complex calculations. In this paper we study ORFs whose numerator and denominator polynomial have real coefficients. These ORFs with real coefficients (RORFs) ap
We ÿrst give a brief summary of the arguments that lead to the conclusion that the use of orthogonal rational functions in system identiÿcation should not be restricted to the Takenaka-Malmquist basis because there are important cases where orthogonality with respect to a certain nonnegative weight
## Abstract This paper contains first steps towards a Szegö theory of orthogonal rational matrix‐valued functions on the unit circle 𝕋. Hereby we are guided by former work of Bultheel, González‐Vera, Hendriksen, and Njåstad on scalar orthogonal rational functions on the one side and by investigatio