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Mixtures of gaussian cylinder set measures and abstract wiener spaces as models for detection of signals imbedded in noise

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Part of the Lecture Notes in Mathematics book series (LNM,volume 656)

Abstract

If one is willing to forget under what restrictions the results of VI. are obtained, the program of III. and IV. has been carried out. To enable one to try to USE such results, the next step is to get rid of the restrictions made. But that has yet unfortunately, to be achieved!

Keywords

  • Gaussian Measure
  • Separable Hilbert Space
  • Reproduce Kernel Hilbert Space
  • Finite Dimensional Hilbert Space
  • Abstract Wiener Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. A. Badrikian and S. Chevet, Mesures cyclindriques, espaces de Wiener et fonctions aléatoires Gaussiennes, Lecture Notes in Math.379, Springer Verlag, Berlin/Heidelberg/New-York, 1974.

    CrossRef  MATH  Google Scholar 

  2. P. Baxendale, Gaussian measures on function spaces, Amer.J.Math., Vol.98(1976),pp.891–952.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. X. Fernique, Intégrabilité des vecteurs Gaussiens, C.R.Acad.Sci. Paris, Vol.270(1970), pp.Al698–9.

    MathSciNet  MATH  Google Scholar 

  4. A. Gleit and J. Zinn, Admissible and singular translates of measures on vector spaces, Trans.Amer.Math.Soc., Vol.221(1976), pp.199–211.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. L. Gross, Measurable functions on Hilbert space, Trans.Amer. Math.Soc.,Vol.105(1962),pp.372–390.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. A.F. Gualtierotti, On the robustness of Gaussian detection, J.Math.Anal.Applic.,Vol.57(1977),pp.20–26.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. G. Kallianpur, Abstract Wiener processes and their reproducing kernel Hilbert spaces, Wahrscheinlichkeitstheorie verw.Geb. Vol.17(1971),pp.113–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. H.H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Math. 463, Springer Verlag, Berlin/Heidelberg/New-York, 1975.

    MATH  Google Scholar 

  9. A.V. Skorohod, Integration in Hilbert space, Springer Verlag, Berlin/Heidelberg/New-York, 1974.

    CrossRef  Google Scholar 

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© 1978 Springer-Verlag

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Gualtierotti, A.F. (1978). Mixtures of gaussian cylinder set measures and abstract wiener spaces as models for detection of signals imbedded in noise. In: Weron, A. (eds) Probability Theory on Vector Spaces. Lecture Notes in Mathematics, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068810

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  • DOI: https://doi.org/10.1007/BFb0068810

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08846-2

  • Online ISBN: 978-3-540-35814-5

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