We consider a semidirect product of two locally compact groups S and T, with S Abelian, denoted by ST. An action of ST on S is introduced to make S a homogeneous space of ST. Then we define a unitary representation from ...

This paper is an investigation of shift invariant subspaces of L2(G), where G is a locally

compact abelian group, or in general a local field, with a compact open subgroup. In

this paper we state necessary ...

In this paper we intoduce a vector-valued inner product on locally compact

abelian groups, which is applicable to time-frequency analysis and Weyl-

Heisenberg frames.

Abstract. Conditions under which a function generates a multiresolution analy-

sis are investigated. The definition of the spectral function of a shift invariant

space is generalized from Rn to a locally compact abelian group...

Conditions under which a function generates a multiresolution analysis are investigated.

We define a new function-valued inner product on L2(G), called phi-product, where G is a locally compact abelian group and phi is a topological isomorphism on G....

if G=H*thou K is the group of semidirect product of two locally compact groups H and K, where K is also abelian, then the quasi regular representation (U,L2(K)) on G is defined.

We define a new function-valued inner product on L2(G), called φ-bracket product, where G is a locally compact abelian group and φ is a topological isomorphism on G. We investigate the notion of φ-orthogonality, Bessel s Inequality and φ...

Most of the interesting groups encountered in the physics literature are semidirect product

groups. These groups are of the general form G = H ×τ K, where H and K are

locally compact groups. In this paper, ...

In this paper we dene a metric on the collection of all trans-
lation invariant spaces on a locally compact abelian group, and we study
some topological properties of the metric space....