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We study a problem of isometric compact 2-step nilmanifolds using some information on their geodesic flows, where is a simply connected 2-step nilpotent Lie group with a left invariant metric and is a cocompact discrete subgroup of isometries of . Among various works concerning this problem, we consider the algebraic aspect of it. In fact, isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, namely by normalizers. So, suitable factorization...
Geometric control theory and Riemannian techniques are used to describe
the reachable set at time t of left invariant single-input control systems
on semi-simple compact Lie groups and to
estimate the minimal time needed to reach any point from identity.
This method provides an effective way to give an upper and a lower bound
for the minimal time needed to transfer a controlled quantum system
with a drift from a given initial position to a given final position.
The bounds include diameters...
There is constructed a compactly generated, separable, locally compact group G and a continuous irreducible unitary representation π of G such that the image π(C*(G)) of the group C*-algebra contains the algebra of compact operators, while the image of the -group algebra does not containany nonzero compact operator. The group G is a semidirect product of a metabelian discrete group and a “generalized Heisenberg group”.
In this paper, we give a concrete method to compute -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over -adic fields. An application to the global setting is also discussed. In particular, we give an explicit -stabilized form of a Saito-Kurokawa lift.
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...
We study a method of approximating representations of the group by those of the group . As a consequence we establish a version of a theorem of DeLeeuw for Fourier multipliers of that applies to the “restrictions” of a function on the dual of to the dual of .
This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
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