Preaspiration (aspiration preceding the closure of a voiceless stop) is typologically rare (Laver 1994: 356) and, in the case of many languages and dialects in North West Europe, is noted as being an areal phenomenon. In some varieties preaspiration has been normalised in the phonology, whereas in others it occurs as a non-obligatory feature (Helgason 2002: 2123). The aim of this paper is to as...

We study direct limits (G,K) = lim −→ (Gn,Kn) of compact Gelfand pairs. First, we develop a criterion for a direct limit representation to be a multiplicityfree discrete direct sum of irreducible representations. Then we look at direct limits G/K = lim −→ Gn/Kn of compact riemannian symmetric spaces, where we combine our criterion with the Cartan–Helgason theorem to show in general that the reg...

This is the first paper in a series of two which proves a version of a theorem of Harish-Chandra for quantum symmetric spaces in the maximally split case: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Here, we est...

Image reconstruction from truncated tomographic data is an important practical problem in CT in order to reduce the X-ray dose and to improve the resolution. The main problem with the Radon Transform is that in 2D the inversion formula globally depends upon line integrals of the object function. The standard Filtered Backprojection algorithm (FBP) does not allow any type of truncation. A typica...

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-be...

in this paper, a new class of multifunctions, called generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions, has been dened and studied. some characterizations and severalproperties concerning generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions are obtained. the re-lationships between generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions and some known con-ce...

The aim of this paper is to establish higher order Poincaré-Sobolev, Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on Siegel domains complex hyperbolic spaces using the method Helgason-Fourier analysis spaces. Firstly, we give a factorization theorem for operators space which closely related Geller's operator, as well CR invariant differential Heisenberg group sphere. (See Theorem 1....

Let σ be a simple involution of an algebraic semisimple group G and let H be the subgroup of G of points fixed by σ. If the restricted root system is of type A,C or BC and G is simply connected or if the restricted root system is of type B and G is adjoint, then we describe a standard monomial theory and the equations for the coordinate ring k[G/H ] using the standard monomial theory and the Pl...