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Bochner Integrals and Neural Networks

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Handbook on Neural Information Processing

Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 49))

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Abstract

A Bochner integral formula \(f = \mathcal{B}-\int_Y w(y)\Phi(y) d\mu(y)\) is derived that presents a function f in terms of weights w and a parametrized family of functions Φ(y), y in Y . Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, G-variation and tensor products are studied, and examples are presented.

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Correspondence to Paul C. Kainen .

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Kainen, P.C., Vogt, A. (2013). Bochner Integrals and Neural Networks. In: Bianchini, M., Maggini, M., Jain, L. (eds) Handbook on Neural Information Processing. Intelligent Systems Reference Library, vol 49. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36657-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-36657-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36656-7

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