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Analytic Continuations of Fourier and Stieltjes Transforms and Generalized Moments of Probability Measures
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hasebe, Takahiro |
| Copyright Year | 2010 |
| Abstract | We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two ways to generalize moments accordingly to Fourier and Stieltjes transforms; however these two turn out to coincide. As applications, we give short proofs of the convergence of probability measures to Cauchy distributions with respect to tensor, free, Boolean and monotone convolutions. |
| Starting Page | 756 |
| Ending Page | 770 |
| Page Count | 15 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10959-011-0344-9 |
| Alternate Webpage(s) | https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/157741/1/yrigk03703.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1009.1510v2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10959-011-0344-9 |
| Volume Number | 25 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
