TY - JOUR
ID - 51181
T1 - On the truncated two-dimensional moment problem
JO - Advances in Operator Theory
JA - AOT
LA - en
SN -
A1 - Zagorodnyuk, Sergey
Y1 - 2018
PY - 2018/04/01
VL - 3
IS - 2
SP - 388
EP - 399
KW - moment problem
KW - Hankel matrix
KW - non-linear inequalities
DO - 10.15352/aot.1708-1212
N2 - We study the truncated two-dimensional moment problem (with rectangular data) to find a non-negative measure $mu(delta)$, $deltainmathfrak{B}(mathbb{R}^2)$, such that $int_{mathbb{R}^2} x_1^m x_2^n dmu = s_{m,n}$, $0leq mleq M,quad 0leq nleq N$, where ${ s_{m,n} }_{0leq mleq M, 0leq nleq N}$ is a prescribed sequence of real numbers; $M,Ninmathbb{Z}_+$. For the cases $M=N=1$ and $M=1, N=2$ explicit numerical necessary and sufficient conditions for the solvability of the moment problem are given. In the cases $M=N=2$; $M=2, N=3$; $M=3, N=2$; $M=3, N=3$ some explicit numerical sufficient conditions for the solvability are obtained. In all the cases some solutions (not necessarily atomic) of the moment problem can be constructed.
UR - http://www.aot-math.org/article_51181.html
L1 - http://www.aot-math.org/pdf_51181_e83e76bde83920b1d8fc1a07b6244513.html
ER -