What Is the Spectral Theory of Random Fields?
We review the current state of the spectral theory of random functions of several variables created by Professor M. I. Yadrenko at the end of 1950s. It turns out that the spectral expansions of multi-dimensional homogeneous and isotropic random fields are governed by a pair of convex compacts and a...
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| Format: | Article |
| Language: | English |
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Austrian Statistical Society
2025-01-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1956 |
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| _version_ | 1841543701652832256 |
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| author | Anatoliy Malyarenko |
| author_facet | Anatoliy Malyarenko |
| author_sort | Anatoliy Malyarenko |
| collection | DOAJ |
| description |
We review the current state of the spectral theory of random functions of several variables created by Professor M. I. Yadrenko at the end of 1950s. It turns out that the spectral expansions of multi-dimensional homogeneous and isotropic random fields are governed by a pair of convex compacts and are especially simple when these compacts are simplexes. Our new result gives necessary and sufficient conditions for such a situation in terms of the group representation that defines the field.
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| format | Article |
| id | doaj-art-826b7f9f0a12460d9565a14e79e59bd8 |
| institution | Kabale University |
| issn | 1026-597X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj-art-826b7f9f0a12460d9565a14e79e59bd82025-01-13T07:12:23ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2025-01-0154110.17713/ajs.v54i1.1956What Is the Spectral Theory of Random Fields?Anatoliy Malyarenko0Professor We review the current state of the spectral theory of random functions of several variables created by Professor M. I. Yadrenko at the end of 1950s. It turns out that the spectral expansions of multi-dimensional homogeneous and isotropic random fields are governed by a pair of convex compacts and are especially simple when these compacts are simplexes. Our new result gives necessary and sufficient conditions for such a situation in terms of the group representation that defines the field. https://www.ajs.or.at/index.php/ajs/article/view/1956 |
| spellingShingle | Anatoliy Malyarenko What Is the Spectral Theory of Random Fields? Austrian Journal of Statistics |
| title | What Is the Spectral Theory of Random Fields? |
| title_full | What Is the Spectral Theory of Random Fields? |
| title_fullStr | What Is the Spectral Theory of Random Fields? |
| title_full_unstemmed | What Is the Spectral Theory of Random Fields? |
| title_short | What Is the Spectral Theory of Random Fields? |
| title_sort | what is the spectral theory of random fields |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1956 |
| work_keys_str_mv | AT anatoliymalyarenko whatisthespectraltheoryofrandomfields |