On Dirac delta sequences and their generating functions

Recently, Galapon [E.A. Galapon, Delta-convergent sequences that vanish at the support of the limit Dirac delta function, J. Phys. A 42 (2009) 175–201] has posed the question of the existence of delta-convergent sequences that vanish at the support of the limit Dirac delta function and gave an example of sequences of this type. It is a sequence of even functions that do not have a compact support. Motivated by the question, in this short note we develop some results concerning delta sequences and show more examples of delta sequences of the type with or without compact support and that are even or not even.