{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T15:45:43Z","timestamp":1775835943259,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540222828","type":"print"},{"value":"9783540278191","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004]]},"DOI":"10.1007\/978-3-540-27819-1_18","type":"book-chapter","created":{"date-parts":[[2010,9,14]],"date-time":"2010-09-14T06:05:39Z","timestamp":1284444339000},"page":"255-269","source":"Crossref","is-referenced-by-count":16,"title":["A Function Representation for Learning in Banach Spaces"],"prefix":"10.1007","author":[{"given":"Charles A.","family":"Micchelli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Massimiliano","family":"Pontil","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"18_CR1","first-page":"57","volume-title":"Proc. of the 17\u2013th Int. Conf. on Machine Learning","author":"K. Bennett","year":"2000","unstructured":"Bennett, K., Bredensteiner: Duality and geometry in support vector machine classifiers. In: Langley, P. (ed.) Proc. of the 17\u2013th Int. Conf. on Machine Learning, pp. 57\u201363. Morgan Kaufmann, San Francisco (2000)"},{"key":"18_CR2","first-page":"89","volume-title":"In Advances in Learning Theory: Methods, Models and ApplicationsNATO Science Series III: Computer and Systems Sciences","author":"S. Canu","year":"2003","unstructured":"Canu, S., Mary, X., Rakotomamonjy, A.: Functional learning through kernel. In: Suykens, J., et al. (eds.) In Advances in Learning Theory: Methods, Models and ApplicationsNATO Science Series III: Computer and Systems Sciences, vol.\u00a0190, pp. 89\u2013110. IOS Press, Amsterdam (2003)"},{"issue":"4","key":"18_CR3","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1007\/BF02837041","volume":"10","author":"J.M. Carnicer","year":"1994","unstructured":"Carnicer, J.M., Bastero, J.: On best interpolation in Orlicz spaces. Approx. Theory and its Appl.\u00a010(4), 72\u201383 (1994)","journal-title":"Theory and its Appl."},{"key":"18_CR4","first-page":"139","volume":"3","author":"W. Dahmen","year":"1987","unstructured":"Dahmen, W., Micchelli, C.A.: Some remarks on ridge functions. Approx. Theory and its Appl.\u00a03, 139\u2013143 (1987)","journal-title":"Approx. Theory and its Appl."},{"key":"18_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9298-9","volume-title":"Best Approximation in inner Product Spaces CMS Books in Mathematics","author":"F. Deutsch","year":"2001","unstructured":"Deutsch, F.: Best Approximation in inner Product Spaces CMS Books in Mathematics. Springer, Heidelberg (2001)"},{"key":"18_CR6","doi-asserted-by":"crossref","unstructured":"Hein, M., Bousquet, O.: Maximal Margin Classification for Metric Spaces. In: Proc. of the 16\u2013th Annual Conference on Computational Learning Theory, COLT (2003)","DOI":"10.1007\/978-3-540-45167-9_7"},{"issue":"1","key":"18_CR7","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0304-3975(95)00021-N","volume":"148","author":"D. Kimber","year":"1995","unstructured":"Kimber, D., Long, P.M.: On-line learning of smooth functions of a single variable. Theoretical Computer Science\u00a0148(1), 141\u2013156 (1995)","journal-title":"Theoretical Computer Science"},{"key":"18_CR8","volume-title":"Approximation of Functions","author":"G.G. Lorenz","year":"1986","unstructured":"Lorenz, G.G.: Approximation of Functions, 2nd edn. Chelsea, New York (1986)","edition":"2"},{"key":"18_CR9","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1162\/15324430260185600","volume":"2","author":"C. Gentile","year":"2001","unstructured":"Gentile, C.: A new approach to maximal margin classification algorithms. Journal of Machine Learning Research\u00a02, 213\u2013242 (2001)","journal-title":"Journal of Machine Learning Research"},{"key":"18_CR10","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","volume":"6","author":"M. Leshno","year":"1993","unstructured":"Leshno, M., Schocken, S.: Multilayer Feedforward Networks with a Non\u2013Polynomial Activation Function can Approximate any Function. Neural Networks\u00a06, 861\u2013867 (1993)","journal-title":"Neural Networks"},{"key":"18_CR11","volume-title":"Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry","author":"J. Matousek","year":"2003","unstructured":"Matousek, J.: Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry. Springer, Berlin (2003)"},{"key":"18_CR12","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/0196-8858(92)90016-P","volume":"13","author":"H.N. Mhaskar","year":"1992","unstructured":"Mhaskar, H.N., Micchelli, C.A.: Approximation by superposition of sigmoidal functions. Advances in Applied Mathematics\u00a013, 350\u2013373 (1992)","journal-title":"Advances in Applied Mathematics"},{"key":"18_CR13","doi-asserted-by":"crossref","unstructured":"Micchelli, C.A., Pontil, M.: A function representation for learning in Banach spaces. Research Note RN\/04\/05, Dept. of Computer Science, UCL (February 2004)","DOI":"10.1007\/978-3-540-27819-1_18"},{"key":"18_CR14","unstructured":"Micchelli, C.A. Pontil, M.: Regularization algorithms for learning theory. Working paper, Dept. of Computer Science, UCL (2004)"},{"key":"18_CR15","doi-asserted-by":"publisher","first-page":"728","DOI":"10.1137\/0909048","volume":"9","author":"C.A. Micchelli","year":"1988","unstructured":"Micchelli, C.A., Utreras, F.I.: Smoothing and interpolation in a convex subset of a hilbert space. SIAM J. of Scientific and Statistical Computing\u00a09, 728\u2013746 (1988)","journal-title":"SIAM J. of Scientific and Statistical Computing"},{"key":"18_CR16","volume-title":"Functional Analysis: An Introduction to Banach Space Theory","author":"T.J. Morrison","year":"2001","unstructured":"Morrison, T.J.: Functional Analysis: An Introduction to Banach Space Theory. John Wiley Inc. New York (2001)"},{"key":"18_CR17","volume-title":"Linear Functional Analysis","author":"W. Orlicz","year":"1990","unstructured":"Orlicz, W.: Linear Functional Analysis. World Scientific, Singapore (1990)"},{"key":"18_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-69894-1","volume-title":"n\u2013Widths in Approximation Theory","author":"A. Pinkus","year":"1985","unstructured":"Pinkus, A.: n\u2013Widths in Approximation Theory. Springer, Ergebnisse (1985)"},{"key":"18_CR19","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1017\/S0962492900002919","volume":"8","author":"A. Pinkus","year":"1999","unstructured":"Pinkus, A.: Approximation theory of the MLP model in neural networks. Acta Numerica\u00a08, 143\u2013196 (1999)","journal-title":"Acta Numerica"},{"key":"18_CR20","volume-title":"Theory of Orlicz Spaces","author":"M.M. Rao","year":"1992","unstructured":"Rao, M.M., Ren, Z.D.R.: Theory of Orlicz Spaces. Marcel Dekker, Inc. New York (1992)"},{"key":"18_CR21","volume-title":"Real Analysis","author":"H.L. Royden","year":"1988","unstructured":"Royden, H.L.: Real Analysis, 3rd edn. Macmillan Publishing Company, New York (1988)","edition":"3"},{"key":"18_CR22","volume-title":"Learning with Kernels","author":"B. Sch\u00f6lkopf","year":"2002","unstructured":"Sch\u00f6lkopf, B., Smola, A.J.: Learning with Kernels. The MIT Press, Cambridge (2002)"},{"key":"18_CR23","volume-title":"The Nature of Statistical Learning Theory","author":"V. Vapnik","year":"1999","unstructured":"Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, New York (1999)","edition":"2"},{"key":"18_CR24","doi-asserted-by":"crossref","unstructured":"von Luxburg, U., Bousquet, O.: Distance\u2013based classification with Lipschitz functions. In: Proc. of the 16\u2013th Annual Conference on Computational Learning Theory, COLT (2003)","DOI":"10.1007\/978-3-540-45167-9_24"},{"key":"18_CR25","doi-asserted-by":"crossref","unstructured":"Wahba, G.: Splines Models for Observational Data. Series in Applied Mathematics, SIAM, Philadelphia, vol.\u00a059 (1990)","DOI":"10.1137\/1.9781611970128"},{"key":"18_CR26","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1023\/A:1012498226479","volume":"46","author":"T. Zhang","year":"2002","unstructured":"Zhang, T.: On the dual formulation of regularized linear systems with convex risks. Machine Learning\u00a046, 91\u2013129 (2002)","journal-title":"Machine Learning"}],"container-title":["Lecture Notes in Computer Science","Learning Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-27819-1_18.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,30]],"date-time":"2024-03-30T11:40:23Z","timestamp":1711798823000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-27819-1_18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004]]},"ISBN":["9783540222828","9783540278191"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-27819-1_18","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004]]}}}