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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2001
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0106056 |
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| _version_ | 1866912364827246592 |
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| author | Frank, Michael Klotz, Lutz P. |
| author_facet | Frank, Michael Klotz, Lutz P. |
| contents | Let W be an integrable positive Hermitian q x q -matrix valued function on the dual group of a discrete abelian group G such that W^{-1} is integrable. Generalizing results of T. Nakazi and of A. G. Miamee and M. Pourahmadi for q=1 we establish a correspondence between trigonometric approximation problems in L^2(W) and certain approximation problems in L^2(W^{-1}). The result is applied to prediction problems for q-variate stationary processes over G, in particular, to the case where G is the group of integers Z. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0106056 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | A duality method in prediction theory of multivariate stationary sequences Frank, Michael Klotz, Lutz P. Probability Functional Analysis 60G25, 60G10, 42A10 Let W be an integrable positive Hermitian q x q -matrix valued function on the dual group of a discrete abelian group G such that W^{-1} is integrable. Generalizing results of T. Nakazi and of A. G. Miamee and M. Pourahmadi for q=1 we establish a correspondence between trigonometric approximation problems in L^2(W) and certain approximation problems in L^2(W^{-1}). The result is applied to prediction problems for q-variate stationary processes over G, in particular, to the case where G is the group of integers Z. |
| title | A duality method in prediction theory of multivariate stationary sequences |
| topic | Probability Functional Analysis 60G25, 60G10, 42A10 |
| url | https://arxiv.org/abs/math/0106056 |