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Zap. Nauchn. Sem. POMI, 2017, Volume 455, Pages 67–83 (Mi znsl6407)  

On biorthogonal $p$-adic wavelet bases

E. J. Kinga, M. A. Skopinab

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-05796-a
Saint Petersburg State University 9.38.198.2015
Volkswagen Foundation


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English version:
Journal of Mathematical Sciences (New York), 2018, 234:2, 158–169

UDC: 517.98+511.225
Received: 10.04.2017

Citation: E. J. King, M. A. Skopina, “On biorthogonal $p$-adic wavelet bases”, Problems in the theory of representations of algebras and groups. Part 31, Zap. Nauchn. Sem. POMI, 455, POMI, St. Petersburg, 2017, 67–83; J. Math. Sci. (N. Y.), 234:2 (2018), 158–169

Citation in format AMSBIB
\Bibitem{KinSko17}
\by E.~J.~King, M.~A.~Skopina
\paper On biorthogonal $p$-adic wavelet bases
\inbook Problems in the theory of representations of algebras and groups. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 455
\pages 67--83
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6407}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 234
\issue 2
\pages 158--169
\crossref{https://doi.org/10.1007/s10958-018-3992-9}


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