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Wavelet Frames to Optimally Learn Functions on Diffusion Measure Spaces

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

Based on the theory of wavelets on data defined manifolds we study the Kolmogorov metric entropy and related measures of complexity of certain function spaces. We also develop constructive algorithms to represent those functions within a prescribed accuracy that is asymptotically optimal up to a logarithmic factor.

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Acknowledgements

M.E. has been funded by the Vienna Science and Technology Fund (WWTF) through project VRG12-009. The authors also thank H.N. Mhaskar for many fruitful discussions.

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Authors and Affiliations

  1. Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Martin Ehler

  2. Faculty of Mathematics, Technische Universität München, Boltzmannstrasse 3, 85748, Garching, Germany

    Frank Filbir

  3. Helmholtz Zentrum München, Ingolstädter Landstrasse 1, 85764, Neuherberg, Germany

    Frank Filbir

Authors
  1. Martin Ehler
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  2. Frank Filbir
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Correspondence to Martin Ehler .

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Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Ehler, M., Filbir, F. (2015). Wavelet Frames to Optimally Learn Functions on Diffusion Measure Spaces. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_78

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