Israel Journal of Mathematics

, Volume 110, Issue 1, pp 189–218

The central limit problem on locally compact groups


  • Riddhi Shah
    • School of MathematicsTata Institute of Fundamental Research

DOI: 10.1007/BF02808181

Cite this article as:
Shah, R. Isr. J. Math. (1999) 110: 189. doi:10.1007/BF02808181


It is shown that the limit μ of a commutative infinitesimal triangular system Δ on a totally disconnected locally compact groupG is embeddable in a continuous one-parameter convolution semigroup if either (1)G is a compact extension of a closed solvable normal subgroup or (2)G is discrete and Δ is normal or (3)G is a discrete linear group over a field of characteristic zero. For a special triangular system of convolution powers\(\left( {\mu _\nu ^{\kappa _\nu } \to \mu ,\mu _n \to \delta _3 } \right)\), the above is shown to hold without any of the conditions (1)–(3). For a general locally compact groupG necessary conditions are obtained for the embeddability of a shift of limit μ of Δ; in particular, the conditions are trivially satisfied whenG is abelian. Also, the embedding of a limit of a symmetric system onG is shown to hold under condition (1) as above.

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© Hebrew University 1999