Geodesic
Spectral analysis of multivariate stationary random functions on some massive groups
Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 177-182.

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The spectral representations for wide sense stationary multivariate random functions and for their covariance functions on two classes of additive vector groups are obtained under some assumptions about continuity of such functions. The first class is nuclear topological groups and the second class is additive group of real vector space equipped with the finite topology.
Keywords: Stationary random functions in Hilbert space, nuclear group, real vector space, spectral representation. 
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Oleksander Ponomarenko; Yuriy Perun. Spectral analysis of multivariate stationary random functions on some massive groups. Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 177-182. http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a11/

[1] A. I. Ponomarenko, Stochastic problems of optimization, Kiev University Press, Kiev, 1980 (Russian)

[2] Y. Kakihara, Multidimensional second order stochastic processes, World Scientific, Singapore, New Jersey, London, Hong Kong, 1997

[3] O. I. Ponomarenko, “To spectral theory of infinite-dimensional homogeneous in wide sense random fields on groups”, Vysnik of Kiev Univ.,sec.math. and mech., 1969, no. 11, 144–121

[4] L. Außenhofer, Contributions to the Duality theory on Topological groups and to the Theory of nuclear groups, Diss. Math., 1999, 389 pp.

[5] L. Außenhofer, “A survey on nuclear groups”, Nuclear groups and Lie groups, Heldermann Verlag Lemgo, 2001, 1–30

[6] W. Banaszczyk, Additive Subgroups of Topological Vector Space, Lecture Notes in Math., 1466, Springer Verlag, Berlin, 1991

[7] H. Glöckner, “Positive definite functions on infinite-dimensional convex cones”, Mem. of AMS, 166:789 (2003)

[8] O. I. Ponomarenko, “Random linear functionals of Second Order I”, Theory Probab. and Math. Stat., 1997, no. 54, 145–154

[9] O. I. Ponomarenko, “Integral representation of random functions with values in locally convex spaces”, Theory Probab. and Math. Stat., 1992, no. 46, 132–141