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2007/2008 Recovery of the Coefficients of Multiple Haar and Walsh Series
Mikhail G. Plotnikov
Real Anal. Exchange 33(2): 291-308 (2007/2008).

Abstract

A family of multidimensional generalized Perron type integrals is constructed. It is shown that these integrals solve the problem of recovering, by generalized Fourier formulae, the coefficients of multiple Haar and Walsh series of some class. This class includes in particular series convergent $\rho$-regularly everywhere except some countable set $E \subset G^{d}$. It is shown that some properties of rectangularly convergent multiple Haar and Walsh series do not hold for the $\rho$-regular convergence.

Citation

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Mikhail G. Plotnikov. "Recovery of the Coefficients of Multiple Haar and Walsh Series." Real Anal. Exchange 33 (2) 291 - 308, 2007/2008.

Information

Published: 2007/2008
First available in Project Euclid: 18 December 2008

zbMATH: 1168.42014
MathSciNet: MR2458247

Subjects:
Primary: 26A39 , 42C25

Keywords: dyadic derivative , dyadic group , Fourier formulae , multiple Haar series , multiple Walsh series , Perron type integral , Sets of uniqueness

Rights: Copyright © 2007 Michigan State University Press

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