Hostname: page-component-7c8c6479df-8mjnm Total loading time: 0 Render date: 2024-03-29T13:09:48.784Z Has data issue: false hasContentIssue false

Contraction subgroups and semistable measures on p-adic Lie groups

Published online by Cambridge University Press:  24 October 2008

S. G. Dani
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Riddhi Shah
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

Extract

Continuous one-parameter semigroups {μt}t≥0 of probability measures on a locally compact group which are semistable with respect to some automorphism τ of the group, namely such that τ(μt) = μct for all t ≥ 0, for a fixed c ∈ (0, 1), have attracted considerable attention of various researchers in recent years (cf. [3], [5] and other references cited therein). A detailed study of semistable measures on (real) Lie groups is carried out in [5]. In this context it is of interest to study semistable measures on the class of p-adic Lie groups, which is another significant class of locally compact groups.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Borel, A.. Linear Algebraic Groups (W. A. Benjamin, 1969).Google Scholar
[2]Cassels, J. W. S.. Local Fields. London Math. Soc. Student Texts 3 (Cambridge University Press, 1986).CrossRefGoogle Scholar
[3]Hazod, W.. Remarks on [semi-] stable probabilities. In Probability Measures on Groups VII. Lecture Notes in Math. vol. 1064 (Springer-Verlag, 1984), pp. 182203.CrossRefGoogle Scholar
[4]Hazod, W. and Siebert, E.. Continuous automorphism groups on a locally compact group contracting modulo a compact subgroup and applications to stable convolution semigroups. Semigroup Forum 33 (1986), 111143.CrossRefGoogle Scholar
[5]Hazod, W. and Siebert, E.. Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups. J. Theoret. Probab. (2) 1 (1988), 211225.CrossRefGoogle Scholar
[6]Heyer, H.. Probability Measures on Locally Compact Groups. A Series of Modern Surveys in Math. no. 94 (Springer-Verlag, 1977).CrossRefGoogle Scholar
[7]Humphreys, J. E.. Linear Algebraic Groups (Springer-Verlag, 1975).CrossRefGoogle Scholar
[8]Serre, J-P.. Lie Algebras and Lie Groups (W. A. Benjamin, 1964).Google Scholar
[9]Siebert, E.. Contractive automorphisms on locally compact groups. Math. Z. 191 (1986), 7390.CrossRefGoogle Scholar
[10]Varadarajan, V. S.. Lie Groups, Lie Algebras, and their Representations. Graduate Texts in Math. no. 102 (Springer-Verlag, 1984).CrossRefGoogle Scholar
[11]Walters, P.. Ergodic Theory. Introductory Lectures. Lecture Notes in Math. no. 458 (Springer-Verlag, 1975).Google Scholar
[12]Wang, S. P.. The Mautner phenomenon for p-adic Lie groups. Math. Z. 185 (1984), 403–11.CrossRefGoogle Scholar
[13]Weil, A.. Basic Number Theory, 2nd ed. (Springer-Verlag, 1973).CrossRefGoogle Scholar