Recovery of the Coefficients of Multiple Haar and Walsh Series
Mikhail G. Plotnikov
Source: Real Anal. Exchange Volume 33, Number 2
(2007), 291-308.
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.
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Keywords: dyadic group; multiple Haar series; multiple Walsh series; dyadic derivative; Perron type integral; Fourier formulae; sets of uniqueness
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rae/1229619408
Mathematical Reviews number (MathSciNet): MR2458247
Zentralblatt MATH identifier: 05499487
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