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Regular orbital measures on Lie algebras

Alex Wright (2008)

Colloquium Mathematicae

Let H₀ be a regular element of an irreducible Lie algebra , and let μ H ₀ be the orbital measure supported on O H ₀ . We show that μ ̂ H ₀ k ∈ L ² ( ) if and only if k > dim /(dim - rank ).

Regularity of convex functions on Heisenberg groups

Zoltán M. Balogh, Matthieu Rickly (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-convexity) are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines.

Relatively weak* closed ideals of A(G), sets of synthesis and sets of uniqueness

A. Ülger (2014)

Colloquium Mathematicae

Let G be a locally compact amenable group, and A(G) and B(G) the Fourier and Fourier-Stieltjes algebras of G. For a closed subset E of G, let J(E) and k(E) be the smallest and largest closed ideals of A(G) with hull E, respectively. We study sets E for which the ideals J(E) or/and k(E) are σ(A(G),C*(G))-closed in A(G). Moreover, we present, in terms of the uniform topology of C₀(G) and the weak* topology of B(G), a series of characterizations of sets obeying synthesis. Finally, closely related to...

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