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On Fourier coefficients with respect to the Walsh double system. (English) Zbl 1301.42011

Summary: We will consider the behavior of Fourier coefficients with respect to the Walsh double system after modification of functions. We prove that for any function \(f(x,y)\in L^p[0,1]^2\) one can find a function \(g\in L^p [0,1]^2\) coinciding with \(f(x,y)\) except a set of small measure such that the non-zero coefficients of \(g(x,y)\) are monotonically decreasing over all rays in absolute value.

MSC:

42A65 Completeness of sets of functions in one variable harmonic analysis
42A20 Convergence and absolute convergence of Fourier and trigonometric series
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