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

Minasyan, A. B.

Proc. Yerevan State Univ., Phys. Math. Sci. 2014, No. 1(233), 22-25 (2014).

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