Indefinite sequences with a finite order singularity in the complex moment problem (Q1204235)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Indefinite sequences with a finite order singularity in the complex moment problem |
scientific article; zbMATH DE number 126353
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Indefinite sequences with a finite order singularity in the complex moment problem |
scientific article; zbMATH DE number 126353 |
Statements
Indefinite sequences with a finite order singularity in the complex moment problem (English)
0 references
3 March 1993
0 references
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.
0 references
complex sequences
0 references
indefinite sequences
0 references
moment problem
0 references
Levy-Khinchin formula
0 references
negative definite sequence
0 references
integral representation
0 references
exponentially bounded sequences
0 references
