| dc.contributor.author |
Anoussis, M |
en |
| dc.contributor.author |
Gatzouras, D |
en |
| dc.date.accessioned |
2014-06-06T06:45:53Z |
|
| dc.date.available |
2014-06-06T06:45:53Z |
|
| dc.date.issued |
2004 |
en |
| dc.identifier.issn |
00018708 |
en |
| dc.identifier.uri |
http://dx.doi.org/10.1016/j.aim.2003.11.001 |
en |
| dc.identifier.uri |
http://62.217.125.90/xmlui/handle/123456789/2692 |
|
| dc.subject |
Compact groups |
en |
| dc.subject |
Fourier transform |
en |
| dc.subject |
Limit theorems for random walks |
en |
| dc.subject |
Spectral radius formula |
en |
| dc.title |
A spectral radius formula for the Fourier transform on compact groups and applications to random walks |
en |
| heal.type |
journalArticle |
en |
| heal.identifier.primary |
10.1016/j.aim.2003.11.001 |
en |
| heal.publicationDate |
2004 |
en |
| heal.abstract |
Let G be a compact group, not necessarily abelian, let Ĝ be its unitary dual, and for f∈L1(G), let fn:f*⋯*f denote n-fold convolution of f with itself and f̂ the Fourier transform of f. In this paper, we derive the following spectral radius formula ||fn||11/n→ maxR∈Ĝ ρ(f̂(R)), where ρ(f̂(R)) is the spectral radius of f̂(R), thereby extending the well-known Beurling-Gelfand spectral radius formula for the Fourier transform on a (locally compact) abelian group. We also establish a partial result in this direction for arbitrary regular Borel measures on G. As applications, we give conceptual and rather short proofs of existing results concerning convergence in the total variation norm of random walks on compact groups, and uniform convergence of the corresponding densities. We also describe how these results may be transferred to homogeneous spaces. © 20003 Elsevier Inc. All rights reserved. |
en |
| heal.journalName |
Advances in Mathematics |
en |
| dc.identifier.issue |
2 |
en |
| dc.identifier.volume |
188 |
en |
| dc.identifier.doi |
10.1016/j.aim.2003.11.001 |
en |
| dc.identifier.spage |
425 |
en |
| dc.identifier.epage |
443 |
en |