Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416948 | Journal of Approximation Theory | 2011 | 15 Pages |
We prove the existence of series âanÏn, whose coefficients (an) are in â©p>1âp and whose terms (Ïn) are translates by rational vectors in Rd 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 W(C0,â1), Cb(Rd), C0(Rd), Lp(Rd), for every pâ[1,â), 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.
⺠The existence of universal series for Wiener's algebra is proved. ⺠The existence of universal series for further function spaces is proved. ⺠The theory of universal series is applied to the heat and Laplace equations.