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Spline Functions and Gaussian Processes (Multidimensional Case)

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Multivariate Approximation Theory

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Abstract

Kimeldorf-Wahba proved in their paper: “Spline functions and stochastic processes” the relationship between certain prediction problems for stochastic processes and spline functions. We will extend this relationship to the multidimensional case.

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References

  1. Groetsch, C.W., Generalized inverses of linear operators, Marcel Dekker Inc. New York — Basel 1977.

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  2. Kimeldorf, G.S. — Wahba, G., Spline functions and stochastic processes, Sankhya: The Indian Journal of Statistics Ser.A Vol.32 (1970), 173–180.

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  3. Lions, J.L. — Magenes, E., Non-homogeneous boundary value problems and applications I, Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Bd. 181, Springer Verlag Berlin Heidelberg — New York 1972.

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  4. Parzen, E., Statistical inference on time series by RKHS methods, Time Ser.stoch.Processes, Convexity combinat.,Proc. twelfth bien.Sem.Canadian math. Congr. 1969 (1970), 1–37.

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  5. Pitt, L.D., A Markov property for Gaussian processes with a multidimensional parameter, J. Rational Mech. and Anal. 43 (1971), 367–391.

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  6. Scheffold, E., Das Spline-Problem als ein Approximations-problem, J. of Approximation Theory 12 (1974) 265–282.

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  7. Schwartz, L., Sous espaces Hilbertiens d’espaces vectoriels topologiques et noyaux associes (noyaux reproduisants), J. Analyse Math. 13 (1961), 115–256.

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Authors
  1. Wolfgang Schlöglmann
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Editors and Affiliations

  1. Lehrstuhl für Mathematik I, Universität Siegen, Hölderlinstraße 3, D-5900, Siegen 21, Western Germany

    Walter Schempp

  2. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen 1, Western Germany

    Karl Zeller

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© 1979 Springer Basel AG

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Schlöglmann, W. (1979). Spline Functions and Gaussian Processes (Multidimensional Case). In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6289-9_23

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  • DOI: https://doi.org/10.1007/978-3-0348-6289-9_23

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1102-5

  • Online ISBN: 978-3-0348-6289-9

  • eBook Packages: Springer Book Archive

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