The two-dimensional moment problem in a strip. (English) Zbl 1289.47032

Zagorodnyuk, S. M.

Methods Funct. Anal. Topol. 19, No. 1, 40-54 (2013).

The author gives a description of all solution measures \(\mu\) of the moment problem \[ \int_\Pi x_1^m x_2^n\, d\mu=s_{m,n},\quad m,n\in \mathbb Z_+, \] where \(\Pi =\{ (x_1,x_2)\in \mathbb R^2: | x_2| \leq R\}\), \(R>0\), \(\{ s_{m,n}\}_{m,n\in \mathbb Z_+}\) is a prescribed sequence of complex numbers. The author uses the operator approach to moment problems and A. V. Shtraus’ theorem on generalized resolvents [Izv. Akad. Nauk SSSR, Ser. Mat. 18, 51–86 (1954; Zbl 0055.10903)].

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

47A57	Linear operator methods in interpolation, moment and extension problems
30E05	Moment problems and interpolation problems in the complex plane
44A60	Moment problems

Keywords:

two-dimensional moment problem; generalized resolvents

Citations:

Zbl 0055.10903