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Comput."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Radial basis function neural networks (RBFNNs) of Hankel translates are essentially linear combinations of translations and dilations of a so-called activation function defined on the nonnegative real axis, where, instead of the standard translation, the modified Delsarte translation operator associated with the Hankel integral transformation of order <jats:inline-formula>\n              <jats:tex-math>$$\\mu &gt; -1\/2$$<\/jats:tex-math>\n            <\/jats:inline-formula> is considered. In this paper, we focus on activation functions <jats:inline-formula>\n              <jats:tex-math>$$\\sigma$$<\/jats:tex-math>\n            <\/jats:inline-formula> such that <jats:inline-formula>\n              <jats:tex-math>$$z^{-\\mu-1\/2}\\sigma(z)$$<\/jats:tex-math>\n            <\/jats:inline-formula> is locally <jats:inline-formula>\n              <jats:tex-math>$$p$$<\/jats:tex-math>\n            <\/jats:inline-formula>-integrable with respect to the measure <jats:inline-formula>\n              <jats:tex-math>$$z^{2 \\mu+1} dz$$<\/jats:tex-math>\n            <\/jats:inline-formula>, for <jats:inline-formula>\n              <jats:tex-math>$$1\\le p &lt; \\infty$$<\/jats:tex-math>\n            <\/jats:inline-formula>. It is shown that such networks enjoy the universal approximation property, that is, are locally dense in <jats:inline-formula>\n              <jats:tex-math>$$p$$<\/jats:tex-math>\n            <\/jats:inline-formula>-mean if, and only if, <jats:inline-formula>\n              <jats:tex-math>$$z^{-\\mu-1\/2}\\sigma(z)$$<\/jats:tex-math>\n            <\/jats:inline-formula> is not an even polynomial. In this way, a result of Nan, Wu, Long, Ma and Sun (2008) that holds true for RBFNNs of standard translates is extended to RBFNNs of Hankel translates.<\/jats:p>","DOI":"10.1007\/s12190-025-02535-8","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T06:23:08Z","timestamp":1750054988000},"page":"1553-1572","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximation by RBF neural networks of Hankel translates with a locally $$p$$-integrable activation function"],"prefix":"10.1007","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9421-9198","authenticated-orcid":false,"given":"Isabel","family":"Marrero","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,16]]},"reference":[{"key":"2535_CR1","doi-asserted-by":"publisher","first-page":"1540","DOI":"10.1016\/j.jat.2012.08.005","volume":"164","author":"C. 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