Nonlinear approximation using rapidly increasing functions. (English) Zbl 0593.41018
Summary: Fix a positive integer n and \(\sigma >0\). For F continuous and positive on [0,\(\infty)\), we consider the space W(n,\(\sigma\) ;F) of functions of the form \(\sum F(\alpha_ jx)P_ j(x)\) where there are m(\(\leq n)\) terms in the sum; the \(P_ j's\) are polynomials of total degree not exceeding n-m; and \(0\leq \alpha_ j\leq \alpha_{j+1}-\sigma\), \(j=1,2,...,m-1\). Under certain conditions on F (primarily that it increase rapidly enough to \(\infty\) as x goes to \(\infty)\), W(n,\(\sigma\) ;F) is an existence space for C[0,1].
MSC:
| 41A30 | Approximation by other special function classes |
| 46A11 | Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) |
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