Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Lukomskii S. F., Kruss I. S. Unitary extension principle on zero-dimensional locally compact groups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2023, vol. 23, iss. 3, pp. 320-338. DOI: 10.18500/1816-9791-2023-23-3-320-338, EDN: AKZMKQ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2023
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Russian
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Article type: 
Article
UDC: 
517.51
EDN: 
AKZMKQ

Unitary extension principle on zero-dimensional locally compact groups

Autors: 
Lukomskii Sergei Feodorovich, Saratov State University
Kruss Iuliia Sergeevna, Saratov State University
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.

Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 22-21-00037, https://rscf.ru/project/22-21-00037/).
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Received: 
16.06.2022
Accepted: 
22.11.2022
Published: 
31.08.2023