On uniformly quasisymmetric groups of circle diffeomorphisms.
On unitary Cauchy filters on topological monoids
For Hausdorff topological monoids, the concept of a unitary Cauchy net is a generalization of the concept of a fundamental sequence of reals. We consider properties and applications of such nets and of corresponding filters and prove, in particular, that the underlying set of a given monoid, endowed with the family of such filters, forms a Cauchy space whose convergence structure defines a uniform topology. A commutative monoid endowed with the corresponding uniformity is uniform. A distant purpose...
On unitary extensions and unitary completions of topological monoids
The concept of a unitary Cauchy net in an arbitrary Hausdorff topological monoid generalizes the concept of a fundamental sequence of reals. We construct extensions of this monoid where all its unitary Cauchy nets converge.
On unitary representations of Jacobi groups.
On universal enveloping algebras in a topological setting
We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups...
On varieties of topological groups generated by solvable groups
On volumes of arithmetic quotients of
We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of . As a result we prove that for any even dimension there exists a unique compact arithmetic hyperbolic -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We...
On weakly almost periodic sets.
On Weyl's reciprocity between group algebras and their commutants
On Whittaker Vectors and Representation Theory.
On zero-dimensionality of subgroups of locally compact groups
Improving the recent result of the author we show that is equivalent to for every subgroup of a Hausdorff locally compact group .
On zeroes of the twisted tensor L-function.
On -level topological groups.
One Parameter Subgroups and Nonstandard Analysis.
One-dimensional K-types in finite dimensional representations of semisimple Lie groups: A generalization of Helgason's theorem.
One-parameter subgroups and the B-C-H formula
An algebraic scheme for Lie theory of topological groups with "large" families of one-parameter subgroups is proposed. Such groups are quotients of "𝔼ℝ-groups", i.e. topological groups equipped additionally with the continuous exterior binary operation of multiplication by real numbers, and generated by special ("exponential") elements. It is proved that under natural conditions on the topology of an 𝔼ℝ-group its group multiplication is described by the B-C-H formula in terms of the associated...
One-parameter submonoids in locally complete differentiable monoids
Open mapping theorems in topological spaces
Open subgroups and Pontryagin duality.
Open subgroups of free topological groups
The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.