E. J. King, M. A. Skopina, “On biorthogonal <nobr>$p$</nobr>-adic wavelet bases”, Zap. Nauchn. Sem. POMI, 2017, Volume 455,Pages <nobr>67

This article is cited in 1 paper

On biorthogonal $p$-adic wavelet bases

E. J. King^a, M. A. Skopina^b

^a University of Bremen, Bremen, Germany
^b St. Petersburg State University, St. Petersburg, Russia

Abstract: 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 $p=2$.

Key words and phrases: $p$-adic multiresolution analysis, scaling function, Riesz basis, $p$-adic wavelets.

UDC: 517.98+511.225

Received: 10.04.2017