Indefinite sequences with a finite order singularity in the complex moment problem
The author shows that indefinite sequences (complex-valued and indexed with two \(d\)-dimensional vectors of natural numbers) that have a singularity of a restricted order are related to the classical moment problem as well as the Levy-Khinchin formula for negative definite sequences. Moreover, an integral representation for these sequences is established, and for exponentially bounded sequences a characterization by finitely many positive definiteness conditions is proved. For a special case, new Levy-Khinchin type integral representations are obtained.
scientific article; zbMATH DE number 126353