Complex moment problem and recursive relations

2016/10/13 by Kaissar Idrissi, Idrissi, Kaissar, El Hassan Zerouali +1
Mathematics · Physics and Astronomy · #44A60 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Primary 47A57 #Quantum chaos and dynamical systems #Secondary 47A20 #math.FA #msc:44A60 #msc:47A20 #msc:47A57

paper · pdf · doi:10.48550/arxiv.1610.03965

23 pages

arxiv created 2016/10/13 · openalex publication_date 2016/10/13 · arxiv updated 2016/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new strategy in solving the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed moment sequences is provided. As a simple application, we obtain a computable solution to the complex moment problem for cubic harmonic characteristic polynomials of the form z³+az+bz, 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 Z³=itZ+uZ 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= ∑_{0≤ n+ m ≤ k} a_nm Zⁿ Z^m (a_nm ∈ ℂ).

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