Walsh-Fourier coefficients of linear mappings (Q2867707)

The author of this paper investigates when a sequence of elements in a quasi-complete locally convex topological vector space \(X\) are the Walsh-Fourier coefficients of a function related to the Cantor group. This paper essentially contains three results.NEWLINENEWLINEFirst, conditions are established for when the sequence of elements in \(X\) are the Walsh-Fourier coefficients of a linear mapping from a homogeneous Banach space on the Cantor group into \(X\). Next, conditions are given for when the sequence of elements in \(X\) are the Walsh-Fourier-Lebesgue coefficients of an integrable function from the Cantor group into \(X\). Finally, a similar result is presented with \(X\) replaced with \(X'\), the conjugate of a separable Banach space, and conditions are given for a sequence of elements in \(X'\) being the Walsh-Fourier-Lebesgue coefficients of a function from the Cantor group into \(X'\).