Abstract
Investigated is quasi-invariance of power probabilities on the infinite product ofSU(2). We consider the subgroup consisting of those actions which keep a measure quasi-invariant (i.e., mutually absolutely continuous) and call it the quasi-invariant subgroup of the measure. We establish several estimations for the quasi-invariant subgroups in terms oflfp-type subgroups ofSU(2)∞. Our methods are based on Hellinger integrals, Fourier analysis, and spherical functions onSU(2).
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References
Hora, A. (1991). Quasi-invariant measures on commutative Lie groups of infinite product type.Math. Z. 206, 169–192.
Okazaki, Y. (1985). Equivalent-singular dichotomy for quasi-invariant ergodic measures.Ann. Inst. Henri Poincaré 21, 393–400.
Shepp, L. A. (1965). Distinguishing a sequence of random variable from a translate of itself.Ann. Math. Stat. 36, 1107–1112.
Shimomura, H. (1976). An aspect of quasi-invariant measures on ℝ∞.Publ. RIMS Kyoto Univ. 11, 749–773.
Vilenkin, N. J. (1968).Special Functions and the Theory of Group Representations. American Mathematical Society.
Yamasaki, Y. (1978).Measures on Infinite Dimensional Spaces, Vol. 2 (in Japanese). Kinokuniya-Shoten, Tokyo.
Yamasaki, Y. (1985).Measures on Infinite Dimensional Spaces. World Scientific, Singapore, Philadelphia.
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Hora, A. Quasi-invariant measures on the infinite product ofSU(2). J Theor Probab 5, 71–100 (1992). https://doi.org/10.1007/BF01046779
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DOI: https://doi.org/10.1007/BF01046779