### A General Character Formula for Irreducible Projections on L2 of a Nilmanifold.

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Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.

For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let ${C}_{c}\left(G\right)$ be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that $({C}_{c}\left(G\right),{\epsilon}_{G})$ has property (FH) if and only if G has property (T). On...

We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this...

Let ${\tau}_{X}$ and ${\tau}_{Y}$ be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that $\Phi \circ {\tau}_{X}\left(t\right)={\tau}_{Y}\left(t\right)\circ \Phi $ for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.

For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras ${A}_{p}(G,\omega )$. For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that...