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Remarks on converse Carleman and Krein criteria for the classical moment problem
| Content Provider | Scilit |
|---|---|
| Author | Pakes, Anthony G. |
| Copyright Year | 2001 |
| Description | The key theme is converse forms of criteria for deciding determinateness in the classical moment problem. A method of proof due to Koosis is streamlined and generalized giving a convexity condition under which moments satisfying implies that c a positive constant. A contrapositive version is proved under a rapid variation condition on f (x), generalizing a result of Lin. These results are used to obtain converses of the Stieltjes versions of the Carleman and Krein criteria. Hamburger versions are obtained which relax the symmetry assumption of Koosis and Lin, respectively. A sufficient condition for Stieltjes determinateness of a discrete law is given in terms of its mass function. These criteria are illustrated through several examples. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B1C73BC6D51C5681A304C4A861863DF9/S1446788700002731a.pdf/div-class-title-remarks-on-converse-carleman-and-krein-criteria-for-the-classical-moment-problem-div.pdf |
| ISSN | 14467887 |
| e-ISSN | 14468107 |
| DOI | 10.1017/s1446788700002731 |
| Journal | Journal of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 71 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2001-08-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society History and Philosophy of Science Primary 44a60 Secondary 26a51 Classical Moment Problem Carleman and Krein Conditions Fenchel Transform Rapid Variation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
