Original sentence: The Bochner-Riesz mean is a summability method often used in harmonic analysis.Then the Bochner-Riesz means  of a function  are defined as
Edited sentence: Analogously, the Bochner-Riesz means  (where  and ) of a general function  on  with Fourier transform  are defined as.As such, in these cases, considering the almost everywhere convergence of Bochner-Riesz means for functions in  spaces is much simpler than the problem of "regular" convergence of Fourier series/integrals.Both definitions can be extended in the obvious way to dimensions higher than 1.For ,  and  may be written as convolution operators, where the convolution kernel is an approximate identity.Loukas Grafakos (2009) Modern Fourier Analysis (Second Edition).Springer, ISBN 9780387094335.The Bochner-Riesz mean is a summability method often used in harmonic analysis when considering convergence of Fourier series and Fourier integrals.Then the Bochner-Riesz means  (where  and ) of a periodic function  with Fourier coefficients  are defined as