Consider the semidirect product group H ×? K, where H and K are two arbitrary locally compact groups and K is also abelian. We introduce the continuous wavelet transform associated to some square integrable representations H ×? K. Moreover, we try to obtain a concrete form for admissible vectors of these integrable representations.

Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic nilmanifold admitting a flat symplectic connection and an infinitesimal automorphism that is not symplectic. On a symplectic manifold (M,Ω), a symplectic connection is a torsion-free affine ...

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the approximations of locally compact groups by more general finite algebraic systems are investigated. It is proved that the approximation of locally compact groups b...

We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on 5 separates the points of S. If X is a Banach space and T: X -* F is a continuous linear operator, then T is quasi-convex if T(U) is quasiconvex, where U is the unit ball of X. In the case when T is compact, T(U) is quasi-convex if and only if it is af...

A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p > 1, say that G has property BPLp if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BPLp and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost...

Pseudoframes for subspaces have been recently introduced by S. Li and H. Ogawa as a tool to analyze lower dimensional data with arbitrary flexibility of both the analyzing and the dual sequence. In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets of parameters. We first introduce a new notion of Beurling dimension for dis...