| Popis: |
Let G be a locally compact abelian group and let M ( G ) be the convolution measure algebra of G. A measure μ ∈ M ( G ) is said to be power bounded if sup n ≥ 0 ‖ μ n ‖ 1 ∞ , where μ n denotes nth convolution power of μ. We show that if μ ∈ M ( G ) is power bounded and A = [ a n , k ] n , k = 0 ∞ is a strongly regular matrix, then the limit lim n → ∞ ∑ k = 0 ∞ a n , k μ k exists in the weak⁎ topology of M ( G ) and is equal to the idempotent measure θ, where θ ˆ = 1 int F μ . Here, θ ˆ is the Fourier-Stieltjes transform of θ, F μ : = { γ ∈ Γ : μ ˆ ( γ ) = 1 } , and 1 int F μ is the characteristic function of int F μ . Some applications are also given. |
