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2023—A twofold commemoration: the 100th birthday of Walsh functions and the 50th anniversary of Professor Joseph Leonard Walsh’s death
In 2023, it is 100 years after the introduction of Walsh functions and 50 years after the death of their introducer Joseph Leonard Walsh. This paper...
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Stability of the Walsh–Hadamard spectrum of cryptographic Boolean functions with biased inputs
We propose a notion of stability of the Walsh–Hadamard spectrum of Boolean functions when inputs are independent and identically distributed...
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On a Vector-Valued Extension of the Littlewood–Paley–Rubio De Francia Inequality for Walsh Functions
In the case of trigonometric system, Rubio de Francia proved the one-sided Littlewood–Paley inequality for arbitrary intervals and for the functions...
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Approximation by Haar and Walsh Polynomials in Weighted Generalized Grand Lebesgue Space
AbstractIn the paper we give direct theorems on approximation by Haar and Walsh polynomials in weighted generalized grand Lebesgue space. Also the...
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On Universal Fourier Series in the Walsh System
We prove some theorems concerning the existence of functions whose Fourier series in the Walsh system are universal in the class of all measurable...
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Numerical approximation of nonlinear stochastic Volterra integral equation based on Walsh function
This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the...
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Finite Parseval Frames in Walsh Analysis
Methods for constructing finite Parseval frames by using Walsh matrices and the discrete Vilenkin–Chrestenson transform are described.
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Two-Dimensional Martingale Transforms and Their Applications in Summability of Walsh–Fourier Series
In the paper, we are going to prove that the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series is bounded...
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Cesàro means with varying parameters of Walsh–Fourier series
In this paper we discuss some convergence and divergence properties of subsequences of Cesàro means with varying parameters of Walsh–Fourier series....
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Maximal operators of Walsh–Nörlund means on the dyadic Hardy spaces
We establish necessary and sufficient conditions for the maximal operator of Walsh–Nörlund means with non-increasing weights to be bounded from the...
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Characterization of Non-Stationary Wavelets and Non-Stationary Multiresolution Analysis Wavelets Related to Walsh Functions
The main aim of the present article is to provide a characteristic description of non-stationary orthonormal wavelets related to Walsh functions...
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Uniform Boundedness of Sequence of Operators Associated with the Walsh System and Their Pointwise Convergence
Revisiting the main point of the almost everywhere convergence, it becomes clear that a weak (1,1)-type inequality must be established for the...
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Littlewood–Paley–Rubio De Francia Inequality for the Two-Parameter Walsh System
A version of Littlewood–Paley–Rubio de Francia inequality for the two-parameter Walsh system is proved: for any family of disjoint rectangles
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Approximation by Haar and Walsh Polynomials in Weighted Variable Exponent Lebesgue Spaces
In the paper, we give direct theorems on approximation by Haar and Walsh polynomials in weighted variable exponent space. Also the degree of...
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Discrete Wavelet Transforms in Walsh Analysis
A review of discrete wavelet transforms defined through Walsh functions and used for image processing, compression of fractal signals, analysis of...