Open Access

# Complex moment problem and recursive relations

### Abstract

We introduce a new methodology to solve the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed \emph{moment} sequences is given. A simple application gives a computable solution to the complex moment problem for cubic harmonic characteristic polynomials of the form $z^3+az+b\overline{z}$, where $a$ and $b$ are arbitrary real numbers. We also recapture a recent result due to Curto-Yoo given for cubic column relations in $M(3)$ of the form $Z^3=itZ+u\overline{Z}$ with $t,u$ real numbers satisfying some suitable inequalities. Furthermore, we solve the truncated complex moment problem with column dependence relations of the form $Z^{k+1}= \sum\limits_{0\leq n+ m \leq k} a_{nm} \overline{Z}^n Z^m$ ($a_{nm} \in \mathbb{C}$).

Key words: Complex moment problem, cubic column relation, recursive doubly indexed sequence, characteristic polynomials in two variables.

### Article Information

 Title Complex moment problem and recursive relations Source Methods Funct. Anal. Topology, Vol. 25 (2019), no. 1, 15-34 MathSciNet MR3935580 Milestones Received 05/03/2017; Revised 06/10/2018 Copyright The Author(s) 2019 (CC BY-SA)

### Authors Information

K. Idrissi
Mohamed V University, Rabat, Morocco

E. H. Zerouali
Mohamed V University, Rabat, Morocco

### Citation Example

K. Idrissi and E. H. Zerouali, Complex moment problem and recursive relations, Methods Funct. Anal. Topology 25 (2019), no. 1, 15-34.

### BibTex

@article {MFAT1141,
AUTHOR = {K. Idrissi and E. H. Zerouali},
TITLE = {Complex moment problem and recursive relations},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {1},
PAGES = {15-34},
ISSN = {1029-3531},
MRNUMBER = {MR3935580},
URL = {http://mfat.imath.kiev.ua/article/?id=1141},
}

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