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Nevanlinna matrices for the strong Stieltjes moment problem

✍ Scribed by Olav Njåstad

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
391 KB
Volume
99
Category
Article
ISSN
0377-0427

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✦ Synopsis

Let {c,,}~ ~ be a doubly infinite sequence of real numbers. A solution of the strong Hamburger moment problem is a positive measure tr on (-~x~, c~) such that c, = f_~ u ~ da(u) for n = 0, ± 1, i 2 ..... A solution of the strong Stieltjes moment problem is a positive measure a on [0, c~z) such that c, = f0 ~ u" da(u) for n =0, 4-1, ±2,.... A moment problem is indeterminate if there exists more than one solution. With an indeterminate strong Hamburger moment problem there is associated a Nevanlinna matrix of functions ct, r, 7, 6 holomorphic in C -{0}. These functions have growth properties partly similar to properties of analogous entire functions associated with an indeterminate classical Hamburger moment problem. In this paper we obtain a stronger growth result in the case where the strong Stieltjes moment problem is solvable. @

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