Spectrality of generalized Sierpinski-type self-affine measures
In this work, we study the spectral property of generalized Sierpinski-type self-affine measures μM,D on R2 generated by an expanding integer matrix M∈M2(Z) with det(M)∈3Z and a non-collinear integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with α1β2−α2β1∈3Z. We give the sufficient and necessary cond...
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| Veröffentlicht in: | Applied and computational harmonic analysis 2021-11, Vol.55, p.129-148 |
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| creator | Liu, Jing-Cheng Zhang, Ying Wang, Zhi-Yong Chen, Ming-Liang |
| description | In this work, we study the spectral property of generalized Sierpinski-type self-affine measures μM,D on R2 generated by an expanding integer matrix M∈M2(Z) with det(M)∈3Z and a non-collinear integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with α1β2−α2β1∈3Z. We give the sufficient and necessary conditions for μM,D to be a spectral measure, i.e., there exists a countable subset Λ⊂R2 such that E(Λ)={e2πi〈λ,x〉:λ∈Λ} forms an orthonormal basis for L2(μM,D). This completely settles the spectrality of the self-affine measure μM,D. |
| doi_str_mv | 10.1016/j.acha.2021.05.001 |
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We give the sufficient and necessary conditions for μM,D to be a spectral measure, i.e., there exists a countable subset Λ⊂R2 such that E(Λ)={e2πi〈λ,x〉:λ∈Λ} forms an orthonormal basis for L2(μM,D). 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We give the sufficient and necessary conditions for μM,D to be a spectral measure, i.e., there exists a countable subset Λ⊂R2 such that E(Λ)={e2πi〈λ,x〉:λ∈Λ} forms an orthonormal basis for L2(μM,D). This completely settles the spectrality of the self-affine measure μM,D.</description><subject>Hadamard triple</subject><subject>Mathematics</subject><subject>Mathematics, Applied</subject><subject>Physical Sciences</subject><subject>Science & Technology</subject><subject>Sierpinski-type self-affine measure</subject><subject>Spectral measure</subject><subject>Spectrum</subject><issn>1063-5203</issn><issn>1096-603X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>HGBXW</sourceid><recordid>eNqNkE1LxDAQhoMouK7-AU-9S-skadIWBJHiFyx42D14C9l0oll325J0lfXXm7KLR_E0M_A-w8xDyCWFjAKV16tMm3edMWA0A5EB0CMyoVDJVAJ_PR57yVPBgJ-SsxBWMUBzUU3I7bxHM3i9dsMu6Wzyhi2O0zc2ydyh710bPlw67HpMAq5tqq11LSYb1GHrMZyTE6vXAS8OdUoWD_eL-imdvTw-13ez1HCAIW14ycucL8GynDEulxVjVSOqykrIjRQlYwZLKLShZW4p2NzyeH1huZGSVnxK2H6t8V0IHq3qvdtov1MU1GhArdRoQI0GFAgVH4zQ1R76wmVng3HYGvwFAaCAopSCxg5ETJf_T9du0IPr2rrbtkNEb_YoRgOf0Zo64I3z0a5qOvfXnT90PoRB</recordid><startdate>202111</startdate><enddate>202111</enddate><creator>Liu, Jing-Cheng</creator><creator>Zhang, Ying</creator><creator>Wang, Zhi-Yong</creator><creator>Chen, Ming-Liang</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>BLEPL</scope><scope>DTL</scope><scope>HGBXW</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1617-0349</orcidid><orcidid>https://orcid.org/0000-0002-2861-9687</orcidid></search><sort><creationdate>202111</creationdate><title>Spectrality of generalized Sierpinski-type self-affine measures</title><author>Liu, Jing-Cheng ; Zhang, Ying ; Wang, Zhi-Yong ; Chen, Ming-Liang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c300t-d383843b0f242236b9229d599f604c65822ce807ac184f10f4f30967f3c66193</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Hadamard triple</topic><topic>Mathematics</topic><topic>Mathematics, Applied</topic><topic>Physical Sciences</topic><topic>Science & Technology</topic><topic>Sierpinski-type self-affine measure</topic><topic>Spectral measure</topic><topic>Spectrum</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Jing-Cheng</creatorcontrib><creatorcontrib>Zhang, Ying</creatorcontrib><creatorcontrib>Wang, Zhi-Yong</creatorcontrib><creatorcontrib>Chen, Ming-Liang</creatorcontrib><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>CrossRef</collection><jtitle>Applied and computational harmonic analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Jing-Cheng</au><au>Zhang, Ying</au><au>Wang, Zhi-Yong</au><au>Chen, Ming-Liang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Spectrality of generalized Sierpinski-type self-affine measures</atitle><jtitle>Applied and computational harmonic analysis</jtitle><stitle>APPL COMPUT HARMON A</stitle><date>2021-11</date><risdate>2021</risdate><volume>55</volume><spage>129</spage><epage>148</epage><pages>129-148</pages><issn>1063-5203</issn><eissn>1096-603X</eissn><abstract>In this work, we study the spectral property of generalized Sierpinski-type self-affine measures μM,D on R2 generated by an expanding integer matrix M∈M2(Z) with det(M)∈3Z and a non-collinear integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with α1β2−α2β1∈3Z. We give the sufficient and necessary conditions for μM,D to be a spectral measure, i.e., there exists a countable subset Λ⊂R2 such that E(Λ)={e2πi〈λ,x〉:λ∈Λ} forms an orthonormal basis for L2(μM,D). This completely settles the spectrality of the self-affine measure μM,D.</abstract><cop>SAN DIEGO</cop><pub>Elsevier Inc</pub><doi>10.1016/j.acha.2021.05.001</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0003-1617-0349</orcidid><orcidid>https://orcid.org/0000-0002-2861-9687</orcidid></addata></record> |
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| subjects | Hadamard triple Mathematics Mathematics, Applied Physical Sciences Science & Technology Sierpinski-type self-affine measure Spectral measure Spectrum |
| title | Spectrality of generalized Sierpinski-type self-affine measures |
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