Universal series induced by approximate identities and some relevant applications Original Research Article

We prove the existence of series image, whose coefficients image are in image and whose terms image are translates by rational vectors in image of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener’s algebra image, image, image, image, for every image, and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions.