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Unitary representations corresponding to measures with bounded support in infinite dimensions

Published online by Cambridge University Press:  20 January 2009

José E. Galé
José E. Galé
Affiliation:
Departamento de Teoria de Funciones, Facultad de Ciencias, Zaragoza, Spain
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Let E be a real Hausdorff locally convex space with topological dual E′, topologised by the strong topology. Let (x, x′) denote the bilinear mapping defining the duality between E and E′ (x∈E, x′∈E′). By a unitary representation of E′ we mean an operator valued function U(x′) = Ux′. defined on E′, whose values are unitary operators in a separable Hilbert space H such that

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 1 , February 1983 , pp. 67 - 72
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

1.Abuabara, T., A version of the Paley–Wiener–Schwartz theorem in Infinite Dimensions, Advances in Holomorphy, Barroso, J. A. (ed.), Proc. of Seminario de Holomorfia (Río de Janeiro 1977) (North–Holland, Amsterdam–New York‐Oxford, 1979), 1–29.Google Scholar
2.Beurling, A. and Malliavin, P., On Fourier transforms of measures with compact support, Ada Math. 107 (1962), 291–309.Google Scholar
3.Colombeau, J. F. and Ansémil, J. M., The Paley–Wiener–Schwartz isomorphism in Nuclearspaces, Rèvue Roumaine de Math. Pures et Appliquées (to appear).Google Scholar
4.Galé, J. E., Sobre espacios de funciones diferenciables en dimensión infinita, aproximables porpolinomios sobre conjuntos acotados (Tesis Doctoral, Facultad de Ciencias, Zaragoza, 1980).Google Scholar
5.Gelfand, I. M. and Vilenkin, N. Ya., Generalized Function, vol. 4. Applications of HarmonicAnalysis (Academic Press, New York–London, 1964).Google Scholar
6.Hogbé-Nlend, H., Théorie des Bornologies et Applications (Lecture Notes in Math. no. 213, Berlin–Heidelberg–New York, 1971).CrossRefGoogle Scholar
7.Ladyzhenskaya, O. A. and Vershik, A. M., Sur 1'évolution des mesures détérminées par les équations de Navier–Stokes et la resolution du probleme de Cauchy pour l'equation statistique de E. Hopf, Annali della Scuola Norm. Sup. di Pisa. Serie IV, 4 (1977), 209–230.Google Scholar
8.Nachbin, L. and Dineen, S., Entire functions of exponential type bounded on the real axis and Fourier transforms of distributions with bounded supports, Israel J. Math. 13 (1976), 321–326.CrossRefGoogle Scholar
9.Pietsch, A., Nuclear Locally Convex Spaces (Ergebnisse der Mathematik und ihrerGrenzgebiete no. 66 (Second Edition), Springer, Berlin–Heidelberg–New York, 1972).Google Scholar
10.Schwarz, L., Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Tata Institute of Fundamental Research (Studies in Math. no. 6, Oxford University Press, 1973).Google Scholar