Spectrality and non-spectrality of a class of Moran measures
Let {Mn}n=1∞∈M2(R) be a sequence of real expanding matrices and {Dn}n=1∞ be a sequence of digit sets withDn={(00),(anbn),(cndn)}, where |andn−bncn|=ϕ(n)∈Z, and letμ{Mn},{Dn}=δM1−1D1⁎δ(M1M2)−1D2⁎δ(M1M2M3)−1D3⁎⋯ be the associated Moran measure. This paper establishes a necessary and sufficient conditi...
Saved in:
| Published in | Journal of mathematical analysis and applications Vol. 543; no. 2; p. 128937 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.03.2025
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Let {Mn}n=1∞∈M2(R) be a sequence of real expanding matrices and {Dn}n=1∞ be a sequence of digit sets withDn={(00),(anbn),(cndn)}, where |andn−bncn|=ϕ(n)∈Z, and letμ{Mn},{Dn}=δM1−1D1⁎δ(M1M2)−1D2⁎δ(M1M2M3)−1D3⁎⋯ be the associated Moran measure. This paper establishes a necessary and sufficient condition for μMn,Dn to be a spectral measure when each Mn is a diagonal matrix, and characterizes the structure of the spectrum Λ. Furthermore, we demonstrate that for any sequence of matrices {Mn}n=1∞ ∈ M2(Z) with det(Mn)∉3Z, the space L2(μ{Mn},{Dn}) contains at most 9 mutually orthogonal exponential functions. The precise maximum cardinality of such functions is also determined. |
|---|---|
| AbstractList | Let {Mn}n=1∞∈M2(R) be a sequence of real expanding matrices and {Dn}n=1∞ be a sequence of digit sets withDn={(00),(anbn),(cndn)}, where |andn−bncn|=ϕ(n)∈Z, and letμ{Mn},{Dn}=δM1−1D1⁎δ(M1M2)−1D2⁎δ(M1M2M3)−1D3⁎⋯ be the associated Moran measure. This paper establishes a necessary and sufficient condition for μMn,Dn to be a spectral measure when each Mn is a diagonal matrix, and characterizes the structure of the spectrum Λ. Furthermore, we demonstrate that for any sequence of matrices {Mn}n=1∞ ∈ M2(Z) with det(Mn)∉3Z, the space L2(μ{Mn},{Dn}) contains at most 9 mutually orthogonal exponential functions. The precise maximum cardinality of such functions is also determined. |
| ArticleNumber | 128937 |
| Author | Wang, Wei-Jie |
| Author_xml | – sequence: 1 givenname: Wei-Jie surname: Wang fullname: Wang, Wei-Jie email: wwjmath@163.com organization: Hubei Key Laboratory of Mathematical Sciences, College of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China |
| BookMark | eNp9j81KxDAUhbMYwZnRF3DVF2jNTdMmhdnI4B-MuFDBXbhNbqClP0NShXl7W8aFK1f3cOE7nG_DVsM4EGM3wDPgUN62WdsjZoILmYHQVa5WbM25EKmQ6vOSbWJsOQcoFKzZ7u1IdgrYNdMpwcElc1ka__xGn2BiO4xxiS9jwCHpCeNXoHjFLjx2ka5_75Z9PNy_75_Sw-vj8_7ukFpRwJRqAbnKNXjtKqdJyYpKWUtlURD5QlQ1ovWeVFEWOVfWOwEkvQNduxzJ5lsmzr02jDEG8uYYmh7DyQA3i7NpzeJsFmdzdp6h3Rmiedl3Q8FE29BgyTVh1jNubP7DfwDKI2R6 |
| Cites_doi | 10.1016/j.acha.2019.12.001 10.1016/0022-1236(74)90072-X 10.1007/s11425-011-4278-6 10.1007/s00605-021-01558-0 10.1016/j.acha.2021.05.001 10.4310/MRL.2004.v11.n2.a8 10.1090/tran/7325 10.1016/j.jfa.2016.10.011 10.1007/BF02788990 10.1007/BF02788699 10.1016/j.jfa.2017.04.003 10.1090/S0002-9939-05-07874-3 10.1016/j.aim.2008.05.004 10.1016/j.jmaa.2013.07.046 10.1515/FORUM.2006.026 10.4310/ACTA.2022.v228.n2.a3 10.1016/j.aim.2014.03.026 10.1016/j.acha.2012.05.003 10.1016/j.jfa.2010.12.001 10.1016/j.aim.2015.07.021 10.1016/j.aim.2012.06.026 10.1016/j.aim.2013.04.016 10.1007/s00041-022-09954-2 10.1016/j.jfa.2013.08.031 10.1007/s00209-007-0104-9 10.1006/jfan.2001.3941 10.1016/j.jmaa.2015.06.064 10.1016/j.jfa.2015.06.013 10.1007/s00041-005-5069-7 10.1016/j.jfa.2008.04.001 10.1016/j.jfa.2018.10.017 |
| ContentType | Journal Article |
| Copyright | 2024 Elsevier Inc. |
| Copyright_xml | – notice: 2024 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.jmaa.2024.128937 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| ExternalDocumentID | 10_1016_j_jmaa_2024_128937 S0022247X2400859X |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 0SF 1B1 1RT 1~. 4.4 457 4G. 5GY 71M 85S 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AAOAW AAQFI AASFE AAXKI AAXUO ABAOU ABJNI ABMAC ABVKL ACDAQ ACGFS ACRLP ADBBV ADEZE AEBSH AEKER AENEX AFJKZ AFKWA AFTJW AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR BKOJK BLXMC CS3 DM4 EBS EFBJH EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA HVGLF IHE IXB J1W KOM LG5 M41 MCRUF MHUIS MO0 N9A O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW T5K TN5 TWZ UPT WH7 XPP YQT ZMT ZU3 ~G- 1~5 29L 5VS 6TJ 7-5 AALRI AAQXK AATTM AAYWO AAYXX ABDPE ABEFU ABFNM ABWVN ABXDB ACRPL ACVFH ADCNI ADFGL ADIYS ADMUD ADNMO ADVLN ADXHL AEIPS AETEA AEUPX AEXQZ AFFNX AFPUW AFXIZ AGCQF AGHFR AGQPQ AGRNS AI. AIGII AIIUN AKBMS AKYEP ANKPU APXCP ASPBG AVWKF AZFZN BNPGV CAG CITATION COF EJD FGOYB G-2 HZ~ H~9 M25 MVM OHT R2- RIG SSH SSZ VH1 VOH WUQ XOL YYP ZCG |
| ID | FETCH-LOGICAL-c251t-82137381f8d9d8e749e64b47ca2eef529baacffe7565307cfd21e4fd18bd3aec3 |
| IEDL.DBID | .~1 |
| ISSN | 0022-247X |
| IngestDate | Tue Jul 01 02:09:46 EDT 2025 Wed Dec 04 16:47:28 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Fourier transform Orthogonal basis Non-spectral measure Spectral measure Moran measure |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c251t-82137381f8d9d8e749e64b47ca2eef529baacffe7565307cfd21e4fd18bd3aec3 |
| ParticipantIDs | crossref_primary_10_1016_j_jmaa_2024_128937 elsevier_sciencedirect_doi_10_1016_j_jmaa_2024_128937 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2025-03-15 |
| PublicationDateYYYYMMDD | 2025-03-15 |
| PublicationDate_xml | – month: 03 year: 2025 text: 2025-03-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of mathematical analysis and applications |
| PublicationYear | 2025 |
| Publisher | Elsevier Inc |
| Publisher_xml | – sequence: 0 name: Elsevier Inc |
| References | An, He, Tao (br0040) 2015; 432 An, He, Lau (br0020) 2015; 283 Jorgensen, Pedersen (br0210) 1998; 75 Dutkay, Jorgensen (br0110) 2007; 256 Ramsey (br0320) 1929; 30 Li (br0250) 2011; 260 Laba, Wang (br0220) 2002; 193 Dai, He, Lau (br0070) 2014; 259 Nathanson (br0190) 1996; vol. 195 Lu, Dong, Zhang (br0300) 2022; 28 Dai, Fu, Yan (br0080) 2021; 52 Lu, Dong (br0290) 2021; 196 Strichartz (br0310) 2000; 81 Dai, He, Lai (br0060) 2013; 242 Deng, Lau (br0090) 2015; 269 Dai (br0050) 2012; 231 Fuglede (br0130) 1974; 16 Kolountzakis, Matolcsi (br0200) 2006; 18 An, He (br0010) 2014; 266 Matolcsi (br0180) 2005; 133 Deng (br0100) 2014; 409 Lev, Matolcsi (br0170) 2022; 228 Liu, Dong, Li (br0260) 2017; 273 Liu, Luo (br0270) 2017; 272 Liu, Zhang, Wang, Chen (br0280) 2021; 55 Farkas, Matolcsi, Mora (br0140) 2006; 12 Li, Wen (br0240) 2012; 55 He, Lai, Lau (br0150) 2013; 34 An, He, He (br0030) 2019; 277 Hu, Lau (br0160) 2008; 219 Li (br0230) 2008; 255 Tao (br0330) 2004; 11 Dutkay, Haussermann, Lai (br0120) 2019; 371 Deng (10.1016/j.jmaa.2024.128937_br0100) 2014; 409 Lu (10.1016/j.jmaa.2024.128937_br0290) 2021; 196 Kolountzakis (10.1016/j.jmaa.2024.128937_br0200) 2006; 18 Dai (10.1016/j.jmaa.2024.128937_br0080) 2021; 52 He (10.1016/j.jmaa.2024.128937_br0150) 2013; 34 Lu (10.1016/j.jmaa.2024.128937_br0300) 2022; 28 An (10.1016/j.jmaa.2024.128937_br0030) 2019; 277 Ramsey (10.1016/j.jmaa.2024.128937_br0320) 1929; 30 Li (10.1016/j.jmaa.2024.128937_br0250) 2011; 260 Dai (10.1016/j.jmaa.2024.128937_br0060) 2013; 242 Deng (10.1016/j.jmaa.2024.128937_br0090) 2015; 269 Dutkay (10.1016/j.jmaa.2024.128937_br0120) 2019; 371 Tao (10.1016/j.jmaa.2024.128937_br0330) 2004; 11 Fuglede (10.1016/j.jmaa.2024.128937_br0130) 1974; 16 An (10.1016/j.jmaa.2024.128937_br0020) 2015; 283 Hu (10.1016/j.jmaa.2024.128937_br0160) 2008; 219 Jorgensen (10.1016/j.jmaa.2024.128937_br0210) 1998; 75 Strichartz (10.1016/j.jmaa.2024.128937_br0310) 2000; 81 Li (10.1016/j.jmaa.2024.128937_br0240) 2012; 55 Dutkay (10.1016/j.jmaa.2024.128937_br0110) 2007; 256 Dai (10.1016/j.jmaa.2024.128937_br0070) 2014; 259 Matolcsi (10.1016/j.jmaa.2024.128937_br0180) 2005; 133 Dai (10.1016/j.jmaa.2024.128937_br0050) 2012; 231 Liu (10.1016/j.jmaa.2024.128937_br0270) 2017; 272 Liu (10.1016/j.jmaa.2024.128937_br0260) 2017; 273 Li (10.1016/j.jmaa.2024.128937_br0230) 2008; 255 Nathanson (10.1016/j.jmaa.2024.128937_br0190) 1996; vol. 195 Farkas (10.1016/j.jmaa.2024.128937_br0140) 2006; 12 An (10.1016/j.jmaa.2024.128937_br0040) 2015; 432 Liu (10.1016/j.jmaa.2024.128937_br0280) 2021; 55 Lev (10.1016/j.jmaa.2024.128937_br0170) 2022; 228 An (10.1016/j.jmaa.2024.128937_br0010) 2014; 266 Laba (10.1016/j.jmaa.2024.128937_br0220) 2002; 193 |
| References_xml | – volume: 371 start-page: 1439 year: 2019 end-page: 1481 ident: br0120 article-title: Hadamard triples generate self-affine spectral measures publication-title: Trans. Am. Math. Soc. – volume: 272 start-page: 599 year: 2017 end-page: 612 ident: br0270 article-title: Spectral property of self-affine measures on publication-title: J. Funct. Anal. – volume: 266 start-page: 343 year: 2014 end-page: 354 ident: br0010 article-title: A class of spectral Moran measures publication-title: J. Funct. Anal. – volume: 242 start-page: 187 year: 2013 end-page: 208 ident: br0060 article-title: Spectral structure of Cantor measures with consecutive digits publication-title: Adv. Math. – volume: 55 start-page: 129 year: 2021 end-page: 148 ident: br0280 article-title: Spectrality of generalized Sierpinski-type self-affine measures publication-title: Appl. Comput. Harmon. Anal. – volume: 255 start-page: 3125 year: 2008 end-page: 3148 ident: br0230 article-title: Non-spectral problem for a class of planar self-affine measures publication-title: J. Funct. Anal. – volume: 283 start-page: 362 year: 2015 end-page: 376 ident: br0020 article-title: Spectrality of a class of infinite convolutions publication-title: Adv. Math. – volume: 75 start-page: 185 year: 1998 end-page: 228 ident: br0210 article-title: Dense analytic subspaces in fractal publication-title: J. Anal. Math. – volume: 273 start-page: 705 year: 2017 end-page: 720 ident: br0260 article-title: Non-spectral problem for the self-affine measures publication-title: J. Funct. Anal. – volume: 256 start-page: 801 year: 2007 end-page: 823 ident: br0110 article-title: Analysis of orthogonality and of orbits in affine iterated function systems publication-title: Math. Z. – volume: vol. 195 year: 1996 ident: br0190 article-title: Elementary Methods in Number Theory publication-title: Graduate Texts in Mathematics – volume: 231 start-page: 1681 year: 2012 end-page: 1693 ident: br0050 article-title: When does a Bernoulli convolution admit a spectrum? publication-title: Adv. Math. – volume: 193 start-page: 409 year: 2002 end-page: 420 ident: br0220 article-title: On spectral Cantor measures publication-title: J. Funct. Anal. – volume: 12 start-page: 483 year: 2006 end-page: 494 ident: br0140 article-title: On Fuglede conjecture and the existence of universal spectra publication-title: J. Fourier Anal. Appl. – volume: 432 start-page: 725 year: 2015 end-page: 732 ident: br0040 article-title: Spectrality of the planar Sierpinski family publication-title: J. Math. Anal. Appl. – volume: 219 start-page: 554 year: 2008 end-page: 567 ident: br0160 article-title: Spectral property of the Bernoulli convolutions publication-title: Adv. Math. – volume: 18 start-page: 519 year: 2006 end-page: 528 ident: br0200 article-title: Tiles with no spectra publication-title: Forum Math. – volume: 196 start-page: 207 year: 2021 end-page: 230 ident: br0290 article-title: Spectrality of a class of Moran measures publication-title: Monatshefte Math. – volume: 409 start-page: 331 year: 2014 end-page: 346 ident: br0100 article-title: Spectrality of one dimensional self-similar measures with consecutive digits publication-title: J. Math. Anal. Appl. – volume: 133 start-page: 3021 year: 2005 end-page: 3026 ident: br0180 article-title: Fuglede's conjecture fails in dimension 4 publication-title: Proc. Am. Math. Soc. – volume: 277 start-page: 255 year: 2019 end-page: 278 ident: br0030 article-title: Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets publication-title: J. Funct. Anal. – volume: 259 start-page: 511 year: 2014 end-page: 531 ident: br0070 article-title: On spectral publication-title: Adv. Math. – volume: 228 start-page: 385 year: 2022 end-page: 420 ident: br0170 article-title: The Fuglede conjecture for convex domains is true in all dimensions publication-title: Acta Math. – volume: 11 start-page: 251 year: 2004 end-page: 258 ident: br0330 article-title: Fuglede's conjecture is false in 5 or higher dimensions publication-title: Math. Res. Lett. – volume: 28 year: 2022 ident: br0300 article-title: Spectrality of some one-dimensional Moran measures publication-title: J. Fourier Anal. Appl. – volume: 52 start-page: 63 year: 2021 end-page: 81 ident: br0080 article-title: Spectrality of self-affine Sierpinski-type measures on publication-title: Appl. Comput. Harmon. Anal. – volume: 16 start-page: 101 year: 1974 end-page: 121 ident: br0130 article-title: Commuting self-adjoint partial differential operators and a group theoretic problem publication-title: J. Funct. Anal. – volume: 30 start-page: 264 year: 1929 end-page: 286 ident: br0320 article-title: On a problem of formal logic publication-title: Proc. Lond. Math. Soc. – volume: 34 start-page: 327 year: 2013 end-page: 338 ident: br0150 article-title: Exponential spectra in publication-title: Appl. Comput. Harmon. Anal. – volume: 81 start-page: 209 year: 2000 end-page: 238 ident: br0310 article-title: Mock Fourier series and transforms associated with certain Cantor measures publication-title: J. Anal. Math. – volume: 260 start-page: 1086 year: 2011 end-page: 1095 ident: br0250 article-title: Spectra of a class of self-affine measures publication-title: J. Funct. Anal. – volume: 269 start-page: 1310 year: 2015 end-page: 1326 ident: br0090 article-title: Sierpinski-type spectral self-similar measures publication-title: J. Funct. Anal. – volume: 55 start-page: 593 year: 2012 end-page: 605 ident: br0240 article-title: Spectrality of planar self-affine measures with two-elements digit set publication-title: Sci. China Math. – volume: 52 start-page: 63 year: 2021 ident: 10.1016/j.jmaa.2024.128937_br0080 article-title: Spectrality of self-affine Sierpinski-type measures on R2 publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2019.12.001 – volume: 16 start-page: 101 year: 1974 ident: 10.1016/j.jmaa.2024.128937_br0130 article-title: Commuting self-adjoint partial differential operators and a group theoretic problem publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(74)90072-X – volume: 55 start-page: 593 year: 2012 ident: 10.1016/j.jmaa.2024.128937_br0240 article-title: Spectrality of planar self-affine measures with two-elements digit set publication-title: Sci. China Math. doi: 10.1007/s11425-011-4278-6 – volume: 196 start-page: 207 issue: 1 year: 2021 ident: 10.1016/j.jmaa.2024.128937_br0290 article-title: Spectrality of a class of Moran measures publication-title: Monatshefte Math. doi: 10.1007/s00605-021-01558-0 – volume: 55 start-page: 129 year: 2021 ident: 10.1016/j.jmaa.2024.128937_br0280 article-title: Spectrality of generalized Sierpinski-type self-affine measures publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2021.05.001 – volume: 11 start-page: 251 year: 2004 ident: 10.1016/j.jmaa.2024.128937_br0330 article-title: Fuglede's conjecture is false in 5 or higher dimensions publication-title: Math. Res. Lett. doi: 10.4310/MRL.2004.v11.n2.a8 – volume: 371 start-page: 1439 issue: 2 year: 2019 ident: 10.1016/j.jmaa.2024.128937_br0120 article-title: Hadamard triples generate self-affine spectral measures publication-title: Trans. Am. Math. Soc. doi: 10.1090/tran/7325 – volume: 272 start-page: 599 year: 2017 ident: 10.1016/j.jmaa.2024.128937_br0270 article-title: Spectral property of self-affine measures on Rn publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2016.10.011 – volume: 81 start-page: 209 year: 2000 ident: 10.1016/j.jmaa.2024.128937_br0310 article-title: Mock Fourier series and transforms associated with certain Cantor measures publication-title: J. Anal. Math. doi: 10.1007/BF02788990 – volume: vol. 195 year: 1996 ident: 10.1016/j.jmaa.2024.128937_br0190 article-title: Elementary Methods in Number Theory – volume: 75 start-page: 185 year: 1998 ident: 10.1016/j.jmaa.2024.128937_br0210 article-title: Dense analytic subspaces in fractal L2-spaces publication-title: J. Anal. Math. doi: 10.1007/BF02788699 – volume: 273 start-page: 705 issue: 2 year: 2017 ident: 10.1016/j.jmaa.2024.128937_br0260 article-title: Non-spectral problem for the self-affine measures publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2017.04.003 – volume: 133 start-page: 3021 issue: 10 year: 2005 ident: 10.1016/j.jmaa.2024.128937_br0180 article-title: Fuglede's conjecture fails in dimension 4 publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-05-07874-3 – volume: 219 start-page: 554 year: 2008 ident: 10.1016/j.jmaa.2024.128937_br0160 article-title: Spectral property of the Bernoulli convolutions publication-title: Adv. Math. doi: 10.1016/j.aim.2008.05.004 – volume: 409 start-page: 331 year: 2014 ident: 10.1016/j.jmaa.2024.128937_br0100 article-title: Spectrality of one dimensional self-similar measures with consecutive digits publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2013.07.046 – volume: 18 start-page: 519 year: 2006 ident: 10.1016/j.jmaa.2024.128937_br0200 article-title: Tiles with no spectra publication-title: Forum Math. doi: 10.1515/FORUM.2006.026 – volume: 228 start-page: 385 year: 2022 ident: 10.1016/j.jmaa.2024.128937_br0170 article-title: The Fuglede conjecture for convex domains is true in all dimensions publication-title: Acta Math. doi: 10.4310/ACTA.2022.v228.n2.a3 – volume: 259 start-page: 511 year: 2014 ident: 10.1016/j.jmaa.2024.128937_br0070 article-title: On spectral N-Bernoulli measures publication-title: Adv. Math. doi: 10.1016/j.aim.2014.03.026 – volume: 34 start-page: 327 issue: 3 year: 2013 ident: 10.1016/j.jmaa.2024.128937_br0150 article-title: Exponential spectra in L2(μ) publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2012.05.003 – volume: 260 start-page: 1086 year: 2011 ident: 10.1016/j.jmaa.2024.128937_br0250 article-title: Spectra of a class of self-affine measures publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2010.12.001 – volume: 283 start-page: 362 year: 2015 ident: 10.1016/j.jmaa.2024.128937_br0020 article-title: Spectrality of a class of infinite convolutions publication-title: Adv. Math. doi: 10.1016/j.aim.2015.07.021 – volume: 231 start-page: 1681 year: 2012 ident: 10.1016/j.jmaa.2024.128937_br0050 article-title: When does a Bernoulli convolution admit a spectrum? publication-title: Adv. Math. doi: 10.1016/j.aim.2012.06.026 – volume: 242 start-page: 187 year: 2013 ident: 10.1016/j.jmaa.2024.128937_br0060 article-title: Spectral structure of Cantor measures with consecutive digits publication-title: Adv. Math. doi: 10.1016/j.aim.2013.04.016 – volume: 28 issue: 4 year: 2022 ident: 10.1016/j.jmaa.2024.128937_br0300 article-title: Spectrality of some one-dimensional Moran measures publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-022-09954-2 – volume: 266 start-page: 343 year: 2014 ident: 10.1016/j.jmaa.2024.128937_br0010 article-title: A class of spectral Moran measures publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2013.08.031 – volume: 256 start-page: 801 year: 2007 ident: 10.1016/j.jmaa.2024.128937_br0110 article-title: Analysis of orthogonality and of orbits in affine iterated function systems publication-title: Math. Z. doi: 10.1007/s00209-007-0104-9 – volume: 193 start-page: 409 issue: 2 year: 2002 ident: 10.1016/j.jmaa.2024.128937_br0220 article-title: On spectral Cantor measures publication-title: J. Funct. Anal. doi: 10.1006/jfan.2001.3941 – volume: 30 start-page: 264 issue: 4 year: 1929 ident: 10.1016/j.jmaa.2024.128937_br0320 article-title: On a problem of formal logic publication-title: Proc. Lond. Math. Soc. – volume: 432 start-page: 725 issue: 2 year: 2015 ident: 10.1016/j.jmaa.2024.128937_br0040 article-title: Spectrality of the planar Sierpinski family publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.06.064 – volume: 269 start-page: 1310 year: 2015 ident: 10.1016/j.jmaa.2024.128937_br0090 article-title: Sierpinski-type spectral self-similar measures publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2015.06.013 – volume: 12 start-page: 483 year: 2006 ident: 10.1016/j.jmaa.2024.128937_br0140 article-title: On Fuglede conjecture and the existence of universal spectra publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-005-5069-7 – volume: 255 start-page: 3125 year: 2008 ident: 10.1016/j.jmaa.2024.128937_br0230 article-title: Non-spectral problem for a class of planar self-affine measures publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2008.04.001 – volume: 277 start-page: 255 issue: 1 year: 2019 ident: 10.1016/j.jmaa.2024.128937_br0030 article-title: Spectrality and non-spectrality of the Riesz product measures with three elements in digit sets publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2018.10.017 |
| SSID | ssj0011571 |
| Score | 2.4468546 |
| Snippet | Let {Mn}n=1∞∈M2(R) be a sequence of real expanding matrices and {Dn}n=1∞ be a sequence of digit sets withDn={(00),(anbn),(cndn)}, where |andn−bncn|=ϕ(n)∈Z, and... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 128937 |
| SubjectTerms | Fourier transform Moran measure Non-spectral measure Orthogonal basis Spectral measure |
| Title | Spectrality and non-spectrality of a class of Moran measures |
| URI | https://dx.doi.org/10.1016/j.jmaa.2024.128937 |
| Volume | 543 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEA6lXvQgPrE-Sg7eJK1Js7sJeCnFUi3tQSzubckTWmgtdj148beb2UdREA-edgkbCN9kZybhm28Qug5hQ4GIDFHMRoQnQhERU0o0N1L5EIB1UeU6mcajGX9Mo7SBBnUtDNAqK99f-vTCW1cj3QrN7no-hxrfENt4kgILUkQyhQp2nsAu73xuaR6gJUNrxXD4uiqcKTlei6UC7SHGO8FNS-iF_ltw-hZwhgdov8oUcb9czCFquNUR2ptsZVY3x-gOuscXVxX5B1Yri8NZnmy-jb16rLCBBBleJ8HcK7wsbwU3J2g2vH8ejEjVDoGYkITkRDAKMkTUCyutcAmXLuaaJ0Yx53zEpFbKeO-SkKOFP9d4y6jj3lKhbU850ztFzbAMd4awvy3OFdKqcPyKe1oZKxWNtDDGxLFhLXRT45CtS9WLrKaDLTJALQPUshK1FopqqLIftsuCW_5j3vk_512gXQZdeIFVF12iZv727q5CapDrdmH7NtrpP4xHU3iOn17GX5QvuZ8 |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1JSwMxFA61HtSDuGJd5-BN0pppZiYBL1IsVTs9tTC3kBVaaC12PHjxt5s3S6kgHrwNYQLhS_KW8L3vIXTr3YYEERksQxNhmjCJWUwIVlRz6bwDVkWVazqKBxP6kkVZA_XqWhigVVa2v7TphbWuRjoVmp3ldAo1vt630SQDFiSLeLaFtqm_vtDGoP215nmAmAypJcPh96pypiR5zeYSxIdC2vZ2mkMz9N-804bH6R-g_SpUDB7L1Ryihl0cob10rbO6OkYP0D6-eKvIPwO5MIFP5vFqY-zNBTLQECHDZ-r3exHMy2fB1Qma9J_GvQGu-iFg7aOQHLOQgA4Rccxww2xCuY2poomWobUuCrmSUjtnEx-k-aurnQmJpc4QpkxXWt09RU2_DHuGAndfJBbcSJ9_xV0lteGSRIppreNYhy10V-MglqXshaj5YDMBqAlATZSotVBUQyV-bJ7wdvmPeef_nHeDdgbjdCiGz6PXC7QbQkteoNhFl6iZv3_YKx8n5Oq6OAffTpG5ig |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Spectrality+and+non-spectrality+of+a+class+of+Moran+measures&rft.jtitle=Journal+of+mathematical+analysis+and+applications&rft.au=Wang%2C+Wei-Jie&rft.date=2025-03-15&rft.issn=0022-247X&rft.volume=543&rft.issue=2&rft.spage=128937&rft_id=info:doi/10.1016%2Fj.jmaa.2024.128937&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jmaa_2024_128937 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-247X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-247X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-247X&client=summon |