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
On Approximation by a Nonfundamental Sequence of Translates
โ Scribed by Badih Ghusayni
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 117 KB
- Volume
- 199
- Category
- Article
- ISSN
- 0022-247X
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โฆ Synopsis
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 ลฝ . represent those functions g t which are in the closure of the linear span of a ร ลฝ .4 ลฝ . nonfundamental sequence f c y t in L R . A result about the degree of n 2 approximation is also proved.
๐ SIMILAR VOLUMES
An approach to the development of a systematic sequence of relativistic approximations is reviewed. The approach depends on the atomically localized nature of relativistic effects, and is based on the normalized elimination of the small component in the matrix modified Dirac equation. Errors in the