Abstract
Fix a positive integern and σ>0. ForF continuous and positive on [0, ∞), we consider the spaceW(n, σ; F) of functions of the form σF(αjx) Pj(x) where there arem(≤n) terms in the sum; theP j's are polynomials of total degree not exceedingn — m; and 0≤αj≤αj+1-α, j=1, 2,⋯, m-1. Under certain conditions onF (primarily that it increase rapidly enough to ∞ asx goes to ∞),W(n, σ; F) is an existence space forC[0,1].
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Communicated by Dietrich Braess.
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Gosselin, R.P. Nonlinear approximation using rapidly increasing functions. Constr. Approx 2, 253–261 (1986). https://doi.org/10.1007/BF01893431
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DOI: https://doi.org/10.1007/BF01893431