Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615178 | Journal of Mathematical Analysis and Applications | 2015 | 15 Pages |
Abstract
We provide an explicit isomorphism between the space of smooth functions E(Rd) and its sequence space representation sâËCN which isomorphically maps various spaces of smooth functions onto their sequence-space representation, including the space D(Rd), of test functions, the space of Schwartz functions S(Rd) and the space of “p-integrable smooth functions” DLp(Rd). By restriction and transposition, this isomorphism yields an isomorphism between the space of distributions Dâ²(Rd) and its sequence space representation sâ²âËÏCN which analogously maps various spaces of distributions isomorphically onto their sequence space representation. We use this isomorphism to construct both a common Schauder basis for these spaces of smooth functions and a common Schauder basis for the corresponding spaces of distributions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Christian Bargetz,