E.A. Pleshcheva. Interpolating orthogonal bases of n-separate MRAs and wavelets ... P. 154-163

Interpolating orthogonal wavelet bases are constructed with the use of several scaling functions. In the classical case, a basis of the space ${L}^2(\mathbb{R})$ is formed by shifts and compressions of a single function $\psi$. In contrast to the classical case, we consider several bases of the space $L^2(\mathbb{R})$, which are formed by shifts and compressions of $n$ functions $\psi^s$, $s=1,\ldots,n$. The $n$-separate wavelets constructed by the author earlier form $n$ orthonormal bases of the space $L^2(\mathbb{R})$. In 2008, Yu.N. Subbotin and N.I. Chernykh suggested a method for modifying the Meyer scaling function in such a way that the basis formed by it is simultaneously orthogonal and interpolating. In the present paper we propose a method for modifying the masks of $n$-separate scaling functions from a wide class in such a way that the resulting new scaling functions and wavelets remain orthogonal and at the same time become interpolating.

Keywords: orthogonal wavelet, interpolating wavelet, scaling function, basis, multiresolution analysis, mask of a scaling function, $n$-separate wavelet

Received September 8, 2022

Revised October 17, 2022

Accepted October 24, 2022

Funding Agency: This study is a part of the research carried out at the Ural Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2022-874).

Ekaterina Aleksandrovna Pleshcheva, Cand. Sci. (Phys.-Math.), Krasovskii Institute of Mathematics and Mechanics of the  Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: eplescheva@gmail.com


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Cite this article as: E.A. Pleshcheva. Interpolating orthogonal bases of n-separate MRAs and wavelets. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 4, pp. 154–163 .