Approximation by Translates of a Positive Definite Function
β Scribed by S.J. Kilmer; W.A. Light; X. Sun; X.M. Yu
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 148 KB
- Volume
- 201
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
Let E be separable q-uniformly smooth Banach space, q ) 1, and let A: Ε½ . D A : E Βͺ E be a K-positive definite operator. Let f g E be arbitrary. An iterative method is constructed which converges strongly to the unique solution of the equation Ax s f. Our result resolves two questions raised by C. E
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 .
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
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}