Unitary extension principle on zero-dimensional locally compact groups
- Авторлар: Lukomskii S.1, Kruss I.1
-
Мекемелер:
- Saratov State University
- Шығарылым: Том 23, № 3 (2023)
- Беттер: 320-338
- Бөлім: Articles
- URL: https://journals.rcsi.science/1816-9791/article/view/250852
- DOI: https://doi.org/10.18500/1816-9791-2023-23-3-320-338
- EDN: https://elibrary.ru/AKZMKQ
- ID: 250852
Дәйексөз келтіру
Толық мәтін
Аннотация
In this article, we obtain methods for constructing step tight frames on an arbitrary locally compact zero-dimensional group. To do this, we use the principle of unitary extension. First, we indicate a method for constructing a step scaling function on an arbitrary zero-dimensional group. To construct the scaling function, we use an oriented tree and specify the conditions on the tree under which the tree generates the mask $m_0$ of a scaling function. Then we find conditions on the masks $m_0, m_1,\ldots , m_q$ under which the corresponding wavelet functions $\psi_1, \psi_2,\ldots ,\psi_q$ generate a tight frame. Using these conditions, we indicate a way of constructing such masks. In conclusion, we give examples of the construction of tight frames.
Авторлар туралы
Sergei Lukomskii
Saratov State University
ORCID iD: 0000-0003-3038-2698
Russia, 410026, Saratov, Astrahanskaya str., 83
Iuliia Kruss
Saratov State University
ORCID iD: 0000-0003-2146-5985
Russia, 410026, Saratov, Astrahanskaya str., 83
Әдебиет тізімі
- Mathematics in Image Processing / ed. by H. Zhao. 2013. 245 p. (IAS/Park City Mathematics Series. Vol. 19). https://doi.org/10.1090/pcms/019
- Ron A., Shen Z. Affine systems in L2(Rd): The analysis of the analysis operator // Journal of Functional Analysis. 1997. Vol. 148, iss. 2. P. 408–447. https://doi.org/10.1006/jfan.1996.3079
- Farkov Y., Lebedeva E., Skopina M. Wavelet frames on Vilenkin groups and their approximation properties // International Journal of Wavelets, Multiresolution and Information Processing. 2015. Vol. 13, iss. 5. 1550036 (19 p.) https://doi.org/10.1142/S0219691315500368
- Shah F. A., Debnath L. Tight wavelet frames on local fields // Analysis. 2013. Vol. 33, iss. 3. P. 293–307. https://doi.org/10.1524/anly.2013.1217
- Ahmad O., Bhat M. Y., Sheikh N. A. Construction of Parseval framelets associated with GMRA on local fields of positive characteristic // Numerical Functional Analysis and Optimization. 2021. Vol. 42, iss. 3. P. 344–370. https://doi.org/10.1080/01630563.2021.1878370
- Albeverio S., Evdokimov S., Skopina M. p-adic multiresolution analysis and wavelet frames // Journal of Fourier Analysis and Applications. 2010. Vol. 16. P. 693–714. https://doi.org/10.1007/s00041-009-9118-5
- Лукомский С. Ф. Кратномасштабный анализ на нульмерных группах и всплесковые базисы // Математическй сборник. 2010. Т. 201, № 5. С. 41–64. https://doi.org/10.4213/sm7580
- Агаев Г. Н., Виленкин Н. Я., Джафарли Г. М., Рубинштейн А. И. Мультипликативные системы функций и гармонический анализ на нульмерных группах. Баку : Элм, 1981. 180 c.
- Albeverio S., Khrennikov A. Yu, Shelkovich V. M. Theory of p-adic Distributions: Linear and Nonlinear Models. Cambridge : Cambridge University Press, 2010. 351 p. https://doi.org/10.1017/CBO9781139107167
- Lukomskii S. F. Step refinable functions and orthogonal MRA on p-adic Vilenkin groups // Journal of Fourier Analysis and Applications. 2014. Vol. 20, iss. 1. P. 42–65. https://doi.org/10.1007/s00041-013-9301-6
- Lukomskii S., Vodolazov A. p-adic tight wavelet frames. 12 mar 2022. https://doi.org/10.48550/arXiv.2203.06352