Real Analysis Exchange

Recovery of the Coefficients of Multiple Haar and Walsh Series

Mikhail G. Plotnikov

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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.

Article information

Source
Real Anal. Exchange Volume 33, Number 2 (2007), 291-308.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.rae/1229619408

Mathematical Reviews number (MathSciNet)
MR2458247

Zentralblatt MATH identifier
05499487

Subjects
Primary: 42C25: Uniqueness and localization for orthogonal series 26A39: Denjoy and Perron integrals, other special integrals

Keywords
dyadic group multiple Haar series multiple Walsh series dyadic derivative Perron type integral Fourier formulae sets of uniqueness

Citation

Plotnikov, Mikhail G. Recovery of the Coefficients of Multiple Haar and Walsh Series. Real Analysis Exchange 33 (2007), no. 2, 291--308. http://projecteuclid.org/euclid.rae/1229619408.


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