Beurling algebras on locally compact groups, tensor products, and multipliers
Beurling-Figà-Talamanca-Herz algebras
For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras . 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...
Beyond the classical Weyl and Colin de Verdière’s formulas for Schrödinger operators with polynomial magnetic and electric fields
We present a pair of conjectural formulas that compute the leading term of the spectral asymptotics of a Schrödinger operator on with quasi-homogeneous polynomial magnetic and electric fields. The construction is based on the orbit method due to Kirillov. It makes sense for any nilpotent Lie algebra and is related to the geometry of coadjoint orbits, as well as to the growth properties of certain “algebraic integrals,” studied by Nilsson. By using the direct variational method, we prove that the...
BGG sequences on spheres
BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called -types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described.
Bigèbres de Lie, doubles et carrés
Biinvariant Operators on Nilpotent Lie Groups.
BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that BZcan be decomposed into a controlled number of pieces, the restriction of f on each of which is quantitatively biLipschitz. This extends a result of [14], which proved the same result, but with the restriction that G has an appropriate discretization. We provide an example of a Carnot group not admitting such...
Billards en polygones et groupes fuchsiens
Bisimple inverse semigroups whose idempotents are an interval.
Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem
It is proved for Abelian groups that the Reidemeister coincidence number of two endomorphisms ϕ and ψ is equal to the number of coincidence points of ϕ̂ and ψ̂ on the unitary dual, if the Reidemeister number is finite. An affirmative answer to the bitwisted Dehn conjugacy problem for almost polycyclic groups is obtained. Finally, we explain why the Reidemeister numbers are always infinite for injective endomorphisms of Baumslag-Solitar groups.
Block additive functions on the Gaussian integers
Blow-up of regular submanifolds in Heisenberg groups and applications
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence...
Bohr compactifications of nonabelian Lie semigroups.
Bol loop actions
The notions of left Bol and Bol-Bruck actions are introduced. A purely algebraic analogue of a Nono family (Lie triple family), the so called Sabinin-Nono family, is given. It is shown that any Sabinin-Nono family is a left Bol-Bruck action. Finally it is proved that any local Nono family is a local left Bol-Bruck action. On general matters see [L.V. Sabinin 91, 99].
Boolean lattices of function algebras on rectangular semigroups.
Borel Structures in Groups and Semigroups.
Bornes inférieures pour les marches aléatoires sur les groupes p-adiques moyennables
Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups
Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.
Boundary Behavior of Harmonic Functions on Symmetric Spaces: Maximal Estimates for Poisson Integrals.