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The Walsh transform of wavelet type systems: divergence almost everywhere. (English) Zbl 1089.42014
It is proved that there exists an integrable function whose Fourier expansion with respect to the Walsh transform of a wavelet type system is divergent a.e. This is an extension of a result by K. S. Kazaryan and A. S. Sargsyan [Izv. Akad. Nauk Arm. SSR, Mat. 24, 403–412 (1989; Zbl 0686.42021)] for the bounded Ciesielski system.
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42C15 General harmonic expansions, frames
40A30 Convergence and divergence of series and sequences of functions
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
41A15 Spline approximation
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
Zbl 0686.42021