Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron
Abstract
:1. Introduction
2. Preliminaries
3. Construction of the Volume Preserving Map and Its Inverse
4. Uniform and Refinable Grids of the Regular Octahedron and of the Ball
4.1. Refinement of the Octahedron
4.1.1. First Step of Refinement
4.1.2. Second Step of Refinement
4.1.3. The General Step of Refinement
4.2. Implementation Issues
4.3. Uniform and Refinable Grids of the Ball
5. Multiresolution Analysis and Piecewise Constant Orthonormal Wavelet Bases of and
- ,
- ,
- The set is an orthonormal basis of the space for each ,
6. Conclusions and Future Works
Author Contributions
Funding
Conflicts of Interest
References
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Holhoş, A.; Roşca, D. Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron. Mathematics 2020, 8, 994. https://doi.org/10.3390/math8060994
Holhoş A, Roşca D. Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron. Mathematics. 2020; 8(6):994. https://doi.org/10.3390/math8060994
Chicago/Turabian StyleHolhoş, Adrian, and Daniela Roşca. 2020. "Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron" Mathematics 8, no. 6: 994. https://doi.org/10.3390/math8060994
APA StyleHolhoş, A., & Roşca, D. (2020). Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron. Mathematics, 8(6), 994. https://doi.org/10.3390/math8060994