The complex moment problem in the exponential form and inverse spectral problems for the block Jacobi type correspondence matrices. (English) Zbl 1258.47025

Dudkin, Mykola E.

Methods Funct. Anal. Topol. 18, No. 2, 111-139 (2012).

The author considers a complex moment problem of the form \[ c_{t,j}=\int_0^\infty \int_0^{2\pi} r^t e^{ij\theta}\,d\rho (r,\theta ),\quad t\in \mathbb Z_+,\;j\in \mathbb Z. \] For this case, an analogue of the correspondence with Jacobi matrices is proposed; there are two corresponding matrices having block three-diagonal structure and acting on the space of \(\ell_2\) type as commuting (bounded) selfadjoint and unitary operators. The moment problem is interpreted in terms of direct and inverse spectral problems for these operators.

Reviewer: Anatoly N. Kochubei (Kyïv)

MSC:

47A57	Linear operator methods in interpolation, moment and extension problems
47B36	Jacobi (tridiagonal) operators (matrices) and generalizations
30E05	Moment problems and interpolation problems in the complex plane

Keywords:

complex moment problem; block three-diagonal matrices; eigenfunction expansion; generalized eigenvector