Equiconvergence of the Riesz means of expansions, corresponding to an n- fold system of exponents and to the n-fold Fourier integral (Q1100380)

The author considers a function f in L 2(G), where G is an N-dimensional rectangular parallelepiped, Riesz means \(\sigma^{\alpha}_{\Lambda}\) of the spectral expansions of the f with respect to an N-fold system of exponential functions and Riesz means \(S^{\alpha}_{\Lambda}\) of the expansions of the f with respect to the N-fold Fourier integral. An estimate of the difference \(| \sigma^{\alpha}_{\Lambda}- S^{\alpha}_{\Lambda}|\) is given. Equiconvergence of both means results from this estimate.