Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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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

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Unitary extension principle on zero-dimensional locally compact groups

Lukomskii Sergei Feodorovich, Saratov State University
Kruss Iuliia Sergeevna, Saratov State University

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.

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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