If f t and its Fourier transform F t satisfy some growth conditions and if c n 0 is a sequence of distinct real numbers satisfying a certain separation condition, we Ε½ . represent those functions g t which are in the closure of the linear span of a Γ Ε½ .4 Ε½ . nonfundamental sequence f c y t in L R .
On Approximation by Translates of Globally Supported Functions
β Scribed by J.J. Lei
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 478 KB
- Volume
- 77
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
β¦ Synopsis
We consider (L_{p})-approximation ( (1 \leqslant p \leqslant \infty) ) from the dilates of a space generated by a finite number of functions that have mild polynomial decay at infinity. In particular, the local-controlled density order of such a family of approximating spaces is characterized in terms of the Strang-Fix condition. 1994 Academic Press, Inc.
π SIMILAR VOLUMES
The problem to be studied goes back to a question of ErdΓΆs and KΓΆvari, concerning functions \(M(x), x \in R_{0}{ }^{+}\), which are positive and logarithmically convex in \(\ln x\). The question to find necessary and sufficient conditions for the existence of a power series \[ N(x)=\sum c_{n} x^{n}