Geodesic
On biorthogonal $p$-adic wavelet bases
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 67-83

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Dual $p$-adic multiresolution analyses (MRAs) generated by scaling test functions are studied. It is proved that if two MRAs are dual, then each of MRAs is the Haar MRA. A characterization of all biorthogonal wavelet systems associated with the Haar MRA is given for the case $p=2$. 
@article{ZNSL_2017_455_a6,
     author = {E. J. King and M. A. Skopina},
     title = {On biorthogonal $p$-adic wavelet bases},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--83},
     publisher = {mathdoc},
     volume = {455},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a6/}
}
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E. J. King; M. A. Skopina. On biorthogonal $p$-adic wavelet bases. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 67-83. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a6/