We investigate the almost everywhere convergence of sequences of convolution operators given by probability measures μₙ on R. If this sequence of operators constitutes an approximate identity on a particular class of functions F, under what additional conditions do we have μₙ f → f a.e. for all f ∈ F? We focus on the particular case of a sequence of contractions Ctₙμ of a single probability measure μ, with tₙ → 0, so that that the sequence of operators is an approximate identity.
No takes yet. Share an insight, caveat, or question.
Parrish et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: