On the factor sets of measures and local tightness of convolution semigroups over Lie groups

Dani, S. G.; McCrudden, M.

doi:10.1007/bf01048725

Cited by 13 publications

(10 citation statements)

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“…For a connected Lie group, by a result of DANI and MCCRUDDEN (cf. [6], Theorem 2.1), any abstract homomorphism from a real directed semigroup is locally tight and hence the preceding conclusion holds without the local tightness assumption. We show that in the case of p-adic algebraic groups also, the conclusion holds without the local tightness assumption (see Theorem 1.5); this includes a p-adic analogue of the result of DANI and MCCRUDDEN.…”

Section: Introductionmentioning

confidence: 70%

“…Since {Z(#,,)},,~M consists of p-adic algebraic groups, it is easy to prove this along the same lines as the proof of Lemma 2.3 in [6]. Now since Z(Z(#~)) is a p-adic algebraic group, without loss of generality we may assume G to be Z(Z(#~)).…”

Section: Theorem 15 Let G Be Any P-adic Algebraic 9roup and Ma(g) Bmentioning

confidence: 93%

“…To prove this theorem we follow some techniques used in the real case by DANI and MCCRUDDEN (cf. [6]) upto a certain extent and then use some results in [21] and some properties of p-adic groups.…”

Section: For a #~Mi(g) F(#)= {2~ml(g)12v=v2=# For Some V~ Mi(g)} Imentioning

confidence: 99%

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Semistable measures and limit theorems on real andp-adic groups

Shah

1993

Monatshefte f�r Mathematik

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Abstract. For any locally compact group G, we show that any locally tight homomorphism from a real directed semigroup into MI(G) (semigroup of probability measures on G) has a 'shift' which extends to a continuous one-parameter semigroup. If G is a p-adic algebraic group then the above holds even iff is not locally tight. These results are applied to give sufficient conditions for embeddability of some translate of limits of sequences of the form {v kn} and # E M 1 (G) such that z(#) = #k, for some k > 1 and zeAut G (cf. Theorems 2.1, 2.4, 3.7).

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Section: Introductionmentioning

confidence: 70%

Section: Theorem 15 Let G Be Any P-adic Algebraic 9roup and Ma(g) Bmentioning

confidence: 93%

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Semistable measures and limit theorems on real andp-adic groups

Shah

1993

Monatshefte f�r Mathematik

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“…The embedding problem (for Lie groups, and such other groups for which the statement may be expected to hold) can be thought to have two components: whether every infinitely divisible μ is rationally embeddable, and whether every rationally embeddable μ is embeddable. The answer to the latter question is known to be in the affirmative, (Dani and McCrudden, 1988). It also seems to this author that from a "practical" point of view this answer may be almost as useful as an affirmative answer to the embedding problem, in the sense that in contexts such as in the study of limit laws, where infinite divisibility can be assured from the context it would also in general be possible to assure rational embeddability of the measure, so to conclude embeddability one would need to appeal only to the weaker statement as in the second part above.…”

Section: Introductionmentioning

confidence: 96%