Geodesic
Interpolating orthogonal bases of n-separate MRAs and wavelets
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 154-163 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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.Ṅ. 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. 
@article{TIMM_2022_28_4_a14,
     author = {E. A. Pleshcheva},
     title = {Interpolating orthogonal bases of n-separate {MRAs} and wavelets},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {154--163},
     year = {2022},
     volume = {28},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a14/}
}
TY  - JOUR
AU  - E. A. Pleshcheva
TI  - Interpolating orthogonal bases of n-separate MRAs and wavelets
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2022
SP  - 154
EP  - 163
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a14/
LA  - ru
ID  - TIMM_2022_28_4_a14
ER  - 
%0 Journal Article
%A E. A. Pleshcheva
%T Interpolating orthogonal bases of n-separate MRAs and wavelets
%J Trudy Instituta matematiki i mehaniki
%D 2022
%P 154-163
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a14/
%G ru
%F TIMM_2022_28_4_a14
E. A. Pleshcheva. Interpolating orthogonal bases of n-separate MRAs and wavelets. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 154-163. http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a14/

[1] Mallat Stéphane G., “Multiresolution approximations and wavelet orthonormal bases of $L^2 (\mathbb{R})$”, Trans. Amer. Math. Soc., 315 (1989), 69–87 | DOI | MR

[2] Meyer Yves, Ondelettes et operateurs: Ondelettes, Hermann, 1990, 215 pp. | MR

[3] Plescheva E.A., “Novoe obobschenie ortogonalnykh bazisov vspleskov”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16:2 (2010), 264–271 | DOI

[4] Berkolaiko M.Z., Novikov I.Ya., “O beskonechno gladkikh pochti-vspleskakh s kompaktnym nositelem”, Mat. zametki, 56:3 (1994), 3–12 | DOI | MR

[5] Zakharov V.G., “Reproducing solutions to PDEs by scaling functions”, Int. J. Wavelets Multiresolut. Inf. Process, 19 (2020), 2050017 | DOI

[6] Subbotin Yu.N., Chernykh N.I., “Interpolyatsionno-ortogonalnye sistemy vspleskov”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14:3 (2008), 153–161 | DOI