Please use this identifier to cite or link to this item:
Title: Infinite convolution products and refinable distributions on lie groups
Authors: Lawton, W. 
Keywords: Cascade sequence
Condition e
Enveloping algebra
Lie group
Refinement operator
Riesz basis
Transition operator
Issue Date: 2000
Citation: Lawton, W. (2000). Infinite convolution products and refinable distributions on lie groups. Transactions of the American Mathematical Society 352 (6) : 2913-2936. ScholarBank@NUS Repository.
Abstract: Sufficient conditions for the convergence in distribution of an infinite convolution product μ1 * μ2 * ... of measures on a connected Lie group G with respect to left invariant Haar measure are derived. These conditions are used to construct distributions φ that satisfy Tφ = φ where T is a refinement operator constructed from a measure n and a dilation automorphism A. The existence of A implies G is nilpotent and simply connected and the exponential map is an analytic homeomorphism. Furthermore', there exists a unique minimal compact subset K. ⊂ G such that for any open set U containing K., and for any distribution f on Q with compact support, there exists an integer n(U, f) such that n ≥ n(U, f) implies supp(Tnf) C U. If μ is supported on an A-invariant uniform subgroup Γ, then T is related, by an intertwining operator, to a transition operator W on C(Γ). Necessary and sufficient conditions for Tn f to converge to φ ∈ L2, and for the Γ-translates of φ to be orthogonal or to form a Riesz basis, are characterized in terms of the spectrum of the restriction of W to functions supported on Ω := KK-1 ⊂ Γ. ©2000 American Mathematical Society.
Source Title: Transactions of the American Mathematical Society
ISSN: 00029947
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

checked on Nov 18, 2021

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.