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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2023, Volume 23, Issue 3, Pages 320–338
DOI: https://doi.org/10.18500/1816-9791-2023-23-3-320-338
(Mi isu987)
 

Scientific Part
Mathematics

Unitary extension principle on zero-dimensional locally compact groups

S. F. Lukomskii, Iu. S. Kruss

Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia
References:
Abstract: 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.
Key words: tight wavelet frames, zero-dimensional groups, refinable functions, trees, unitary extension principle.
Funding agency Grant number
Russian Science Foundation 22-21-00037
This work was supported by the Russian Science Foundation (project No. 22-21-00037, https://rscf.ru/project/22-21-00037/).
Received: 16.06.2022
Accepted: 22.11.2022
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: S. F. Lukomskii, Iu. S. Kruss, “Unitary extension principle on zero-dimensional locally compact groups”, Izv. Saratov Univ. Math. Mech. Inform., 23:3 (2023), 320–338
Citation in format AMSBIB
\Bibitem{LukKru23}
\by S.~F.~Lukomskii, Iu.~S.~Kruss
\paper Unitary extension principle on~zero-dimensional~locally~compact~groups
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2023
\vol 23
\issue 3
\pages 320--338
\mathnet{http://mi.mathnet.ru/isu987}
\crossref{https://doi.org/10.18500/1816-9791-2023-23-3-320-338}
\edn{https://elibrary.ru/AKZMKQ}
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    Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
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