Summary
Our aim is to extend Schoenberg's classical theorem to higher dimensions, by establishing representations of arbitrary separately or jointly rotatable continuous linear random functionals in terms of multiple Wiener-Itô integrals and their tensor products. This leads to similar representations for separately or jointly rotatable arrays, and for separately or jointly exchangeable or spreadable random sheets.
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Research supported by NSF Grant DMS-9103050
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Kallenberg, O. Random arrays and functionals with multivariate rotational symmetries. Probab. Th. Rel. Fields 103, 91–141 (1995). https://doi.org/10.1007/BF01199033
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DOI: https://doi.org/10.1007/BF01199033