 Author
 Year
 2008
 Title
 An indeterminate rational moment problem and Carathéodory functions
 Journal
 Journal of Computational and Applied Mathematics
 Volume  Issue number
 219  2
 Pages (fromto)
 359369
 Document type
 Article
 Faculty
 Faculty of Science (FNWI)
 Institute
 Kortewegde Vries Institute for Mathematics (KdVI)
 Abstract

Let {alpha(n)}(n=1)(infinity) be a sequence of points in the open unit disk in the complex plane and let
B0 = 1 and Bn(Z) = Pi(n)(k=0) (alpha(k)) over bar/vertical bar alpha(k)vertical bar alpha(k) 
z/1alpha(k)z, n = 1,2, ...,
((alpha(k)) over bar/vertical bar alpha(k)vertical bar =  1 when alpha(k) = 0). We put L = span{Bn : n =
0,1,2, ...} and we consider the following "moment" problem: Given a positivedefinite Hermitian inner product
<.,.> in L, find all positive Borel measure v on [pi, pi) such that
< f,g > = integral(pi)(pi) f(e(i0))<(g(e(i0)))over bar>dv(0) for f,g epsilon L.
We assume that this moment problem is indeterminate. Under some additional condition on the alpha(n) we will describe a onetoone correspondence between the collection of all solutions to this moment problem and the collection of all Caratheodory functions augmented by the constant infinity.  URL
 go to publisher's site
 Language
 Undefined/Unknown
 Permalink
 http://hdl.handle.net/11245/1.292341
Disclaimer/Complaints regulations
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.