Nonspectrality of Certain Self-Affine Measures on ℝ3
We will determine the nonspectrality of self-affine measure μB,D corresponding to B=diag[p1,p2,p3] (p1∈(2ℤ+1)∖{±1}, p2∈2ℤ∖{0}), and D={0,e1,e2,e3} in the space ℝ3 is supported on T(B,D), where e1, e2, and e3 are the standard basis of unit column vectors in ℝ3, and there exist at most 4 mutually or...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/294182 |
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| author | Gui-Bao Gao |
| author_facet | Gui-Bao Gao |
| author_sort | Gui-Bao Gao |
| collection | DOAJ |
| description | We will determine the nonspectrality of self-affine measure μB,D corresponding to B=diag[p1,p2,p3] (p1∈(2ℤ+1)∖{±1}, p2∈2ℤ∖{0}), and D={0,e1,e2,e3} in the space ℝ3 is supported on T(B,D), where e1, e2, and e3 are the standard basis of unit column vectors in ℝ3, and there exist at most 4 mutually orthogonal exponential functions in L2(μB,D), where the number 4 is the best. This generalizes the known results on the spectrality of self-affine measures. |
| format | Article |
| id | doaj-art-4ebf510324c6459f8e5ef96a60b6353a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4ebf510324c6459f8e5ef96a60b6353a2025-02-03T01:10:48ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/294182294182Nonspectrality of Certain Self-Affine Measures on ℝ3Gui-Bao Gao0College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaWe will determine the nonspectrality of self-affine measure μB,D corresponding to B=diag[p1,p2,p3] (p1∈(2ℤ+1)∖{±1}, p2∈2ℤ∖{0}), and D={0,e1,e2,e3} in the space ℝ3 is supported on T(B,D), where e1, e2, and e3 are the standard basis of unit column vectors in ℝ3, and there exist at most 4 mutually orthogonal exponential functions in L2(μB,D), where the number 4 is the best. This generalizes the known results on the spectrality of self-affine measures.http://dx.doi.org/10.1155/2014/294182 |
| spellingShingle | Gui-Bao Gao Nonspectrality of Certain Self-Affine Measures on ℝ3 Abstract and Applied Analysis |
| title | Nonspectrality of Certain Self-Affine Measures on ℝ3 |
| title_full | Nonspectrality of Certain Self-Affine Measures on ℝ3 |
| title_fullStr | Nonspectrality of Certain Self-Affine Measures on ℝ3 |
| title_full_unstemmed | Nonspectrality of Certain Self-Affine Measures on ℝ3 |
| title_short | Nonspectrality of Certain Self-Affine Measures on ℝ3 |
| title_sort | nonspectrality of certain self affine measures on r3 |
| url | http://dx.doi.org/10.1155/2014/294182 |
| work_keys_str_mv | AT guibaogao nonspectralityofcertainselfaffinemeasuresonr3 |