Graded nilpotent Lie algebra of rank 3 and inverse of a differential operator. (Algèbre de Lie nilpotente graduée de rang 3 et inverse d'un opérateur différentiel.)
Group C*-algebras satisfying Kadison's conjecture
We tackle R. V. Kadison’s similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison’s problem) and thereby we establish some stability results for Kadison’s problem. Namely, we prove that inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove that G/Γ is...
Group ideals in a semigroup of measures.
Group reflection and precompact paratopological groups
We construct a precompact completely regular paratopological Abelian group G of size (2ω)+ such that all subsets of G of cardinality ≤ 2ω are closed. This shows that Protasov’s theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups. We also prove that the group reflection of the product of an arbitrary family of paratopological (even semitopological) groups is topologically isomorphic to the product of the group reflections of the factors,...
Group representations by automorphisms of a proposition system
Group representations of bounded cosine functions.
Group Representations which Vanish at Infinity.
Groupes localement compacts
Groupoid -algebras.
Groups of Measure Preserving Transformations.
Groups of Measure Preserving Transformations. II.
Growth and smooth spectral synthesis in the Fourier algebras of Lie groups
Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate...
estimates for weakly strongly singular integral operators on spaces of homogeneous type
Haar null and non-dominating sets
We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of . Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain...
Haar system on a product of zero-dimensional compact groups
In this work, we study the problem of constructing Haar bases on a product of arbitrary compact zero-dimensional Abelian groups. A general scheme for the construction of Haar functions is given for arbitrary dimension. For dimension d=2, we describe all Haar functions.
Haar wavelets on the Lebesgue spaces of local fields of positive characteristic
We construct the Haar wavelets on a local field K of positive characteristic and show that the Haar wavelet system forms an unconditional basis for , 1 < p < ∞. We also prove that this system, normalized in , is a democratic basis of . This also proves that the Haar system is a greedy basis of for 1 < p < ∞.
Hahn's Embedding Theorem for orders and harmonic analysis on groups with ordered duals
Let G be a locally compact abelian group whose dual group Γ contains a Haar measurable order P. Using the order P we define the conjugate function operator on , 1 ≤ p < ∞, as was done by Helson [7]. We will show how to use Hahn’s Embedding Theorem for orders and the ergodic Hilbert transform to study the conjugate function. Our approach enables us to define a filtration of the Borel σ-algebra on G, which in turn will allow us to introduce tools from martingale theory into the analysis on groups...
Hajłasz-Sobolev type spaces and -energy on the Sierpinski gasket.
Hankel forms
It is an open question whether Nehari's theorem on the circle group has an analogue on the infinite-dimensional torus. In this note it is shown that if the analogue holds, then some interesting inequalities follow for certain trigonometric polynomials on the torus. We think these inequalities are false but are not able to prove that.
Hankel forms and sums of random variables
A well known theorem of Nehari asserts on the circle group that bilinear forms in H² can be lifted to linear functionals on H¹. We show that this result can be extended to Hankel forms in infinitely many variables of a certain type. As a corollary we find a new proof that all the norms on the class of Steinhaus series are equivalent.