Name
Abstract | ||
|---|---|---|
In the paper "Approximation by Superpositions of a SigmoidaI Function" [C], the proof given for Lemma i is incorrect since it relies on the erroneous statement that simple functions are dense in L=(R). The author has pointed out that the proof in I'C] can be corrected by changing, at the bottom of page 307 and the top of page 308, the occurrences of L~(R) to L=(J) for a compact interval, J, containing {yrxlx ~ I,}, where y is fLxed. It should also be noted that the reduction of multidimensional density to one-dimensional density as in the proof of Lemma 1 had previously been obtained by Dahmen and Micchelli, using the same techniques, in work on ridge regression (see Lemma 3.2 of [DM]). We thank Raymond T, Melton, who pointed out the error in the proof of Lemma 1 in [C] and supplied a proof, showing that the Fourier transform of the measure /~ must be zero because the/~-measure of every half-plane is zero [M]. |
Year | DOI | Venue |
|---|---|---|
1992 | 10.1007/BF02134016 | MCSS |
DocType | Volume | Issue |
Journal | 5 | 4 |
Citations | PageRank | References |
24 | 26.41 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hrushikesh Narhar Mhaskar | 1 | 257 | 61.07 |
| C A Micchelli | 2 | 49 | 37.15 |