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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
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.
Received: 16.06.2022 Accepted: 22.11.2022
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
Linking options:
https://www.mathnet.ru/eng/isu987 https://www.mathnet.ru/eng/isu/v23/i3/p320
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Statistics & downloads: |
Abstract page: | 68 | Full-text PDF : | 36 | References: | 16 |
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