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Nonuniform Multiwavelet Sets and Multiscaling Sets |
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| Authors: | Shiva Mittal Niraj K. Shukla Nadya A. S. Atlouba |
| Affiliation: | 1. Department of Mathematics, Shyama Prasad Mukherjee Govt. Degree College, Allahabad, Indiashivamittal009@gmail.com;3. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, India;4. Department of Mathematics, Sam Higginbottom Institute of Agriculture, Technology and Sciences, Deemed to be University, Allahabad, India |
| Abstract: | In this article, we study the theory of nonuniform minimally supported frequency multiwavelets and nonuniform multiscaling sets. A characterization of nonuniform multiwavelet sets is obtained which generalizes a result of Yu and Gabardo. After introducing a notion of generalized nonuniform scaling set, we obtain a characterization of nonuniform multiscaling sets associated with nonuniform multiresolution analysis having finite multiplicity. In addition, we provide a geometric construction to find families of symmetric nonuniform multiwavelet sets. |
| Keywords: | Generalized scaling sets multiscaling sets multiwavelets multiwavelet sets nonuniform multiresolution analysis (NUMRA) nonuniform multiresolution analysis with multiplicity D (NUMRA-D) spectral pairs |