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# Indefinite moment problem as an abstract interpolation problem

### Abstract

Indefinite moment problem was considered by M. G. Krein and H. Langer in 1979. In the present paper the general indefinite moment problem is associated with an abstract interpolation problem in generalized Nevanlinna classes. To prove the equivalence of these two problems we investigate the structure of de Branges space $H(m)$ associated with a generalized Nevanlinna function $m$. A general formula for description of the set of solutions of indefinite moment problem is found. It is shown that the Kein-Langer description can be derived from this formula by a special choice of biorthogonal system of polynomials.

Key words: Moment problem, abstract interpolation problem, reproducing kernel space, de Branges space, generalized Nevanlinna function.

### Article Information

 Title Indefinite moment problem as an abstract interpolation problem Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 2, 168-186 MathSciNet MR3098495 zbMATH 1289.47030 Milestones Received 05/02/2013 Copyright The Author(s) 2013 (CC BY-SA)

### Authors Information

Evgen Neiman
Lyceum at Donetsk National University, 46 Schorsa, Donetsk, 83050, Ukraine

### Citation Example

Evgen Neiman, Indefinite moment problem as an abstract interpolation problem, Methods Funct. Anal. Topology 19 (2013), no. 2, 168-186.

### BibTex

@article {MFAT680,
AUTHOR = {Neiman, Evgen},
TITLE = {Indefinite moment problem as an abstract interpolation problem},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {2},
PAGES = {168-186},
ISSN = {1029-3531},
MRNUMBER = {MR3098495},
ZBLNUMBER = {1289.47030},
URL = {http://mfat.imath.kiev.ua/article/?id=680},
}