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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
P. Baxendale, Gaussian measures on function spaces, Amer.J.Math., Vol.98(1976),pp.891–952.
X. Fernique, Intégrabilité des vecteurs Gaussiens, C.R.Acad.Sci. Paris, Vol.270(1970), pp.Al698–9.
A. Gleit and J. Zinn, Admissible and singular translates of measures on vector spaces, Trans.Amer.Math.Soc., Vol.221(1976), pp.199–211.
L. Gross, Measurable functions on Hilbert space, Trans.Amer. Math.Soc.,Vol.105(1962),pp.372–390.
A.F. Gualtierotti, On the robustness of Gaussian detection, J.Math.Anal.Applic.,Vol.57(1977),pp.20–26.
G. Kallianpur, Abstract Wiener processes and their reproducing kernel Hilbert spaces, Wahrscheinlichkeitstheorie verw.Geb. Vol.17(1971),pp.113–123.
H.H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Math. 463, Springer Verlag, Berlin/Heidelberg/New-York, 1975.
A.V. Skorohod, Integration in Hilbert space, Springer Verlag, Berlin/Heidelberg/New-York, 1974.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0068810
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08846-2
Online ISBN: 978-3-540-35814-5
eBook Packages: Springer Book Archive
