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Lindeberg-Feller theorems on Lie groups

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Abstract.

Necessary and sufficient conditions are given for a triangular array of probability measures on an arbitrary Lie group to converge to a Gauss measure. The main step of the proofs is an estimation for the Fourier transform of a probability measure in terms of integrals of local coordinates and a Hunt function, suggested by Professor E. Siebert. The special case of stratified nilpotent Lie groups is investigated separately.

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Authors and Affiliations

  1. Institute of Mathematics, Lajos Kossuth University, Pf. 12, H-4010 Debrecen, Hungary, , , , , , HU

    G. Pap

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  1. G. Pap
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Received: 4.3.1998

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Pap, G. Lindeberg-Feller theorems on Lie groups. Arch. Math. 72, 328–336 (1999). https://doi.org/10.1007/s000130050340

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  • DOI: https://doi.org/10.1007/s000130050340

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