On a problem of Freudenthal's
On a problem of Narkiewicz concerning uniform distributions of sequences of integers
On a property of the one-dimensional torus
On a quantitative version of the Oppenheim conjecture.
On a semigroup of measures with irregular densities
We study the densities of the semigroup generated by the operator on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are . We give explicit spectral decomposition of images of in representations.
On a special class of Frobenius groups admitting planar partitions.
On a theorem of S. Banach.
On a theorem of van Douwen.
On a theorem of W.W. Comfort and K.A. Ross
A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group and prove that every -dense subspace of a topological group , such...
On a translation property of positive definite functions
If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant such that for every continuous positive definite g≥0, where is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That “for one h” implies “for all h” seemed obvious, but turned out not to be obvious at all. We fill...
On a universality property of some abelian Polish groups
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
On a variant of Kazhdan's property (T) for subgroups of semisimple groups
Let be an irreducible lattice in a product of simple groups. Assume that has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of in terms of the topology of the dual space of .We use this result to give a new proof for the triviality of the first cohomology group of with coefficients in a finite dimensional unitary representation.
On additive number-theoretical functions with values in a compact Abelian group.
On algebraic Anosov diffeomorphisms on nilmanifolds.
On algebraic radicals in mobs
On Algebras all of Whose Subalgebras are Simple; Some Solutions of Plonka's Problem
On Amenable and Compact Groups.
On an application of the work of D.E. Knuth to semigroups.
On an extension of a theorem of Tunnell
On Analytic Vectors for Unitary Representations of Infinite Dimensional Lie Groups
Let be a connected and simply connected Banach–Lie group. On the complex enveloping algebra of its Lie algebra we define the concept of an analytic functional and show that every positive analytic functional is integrable in the sense that it is of the form for an analytic vector of a unitary representation of . On the way to this result we derive criteria for the integrability of -representations of infinite dimensional Lie algebras of unbounded operators to unitary group representations.For...