‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

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.

We complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups. The torsion-free part of the group is free abelia...

3 W . H A A S , J . ADAMS, a n d J . B . FLANNERY, P h y s . R e v . L e t ters 25, 1326 [1970]. 4 Deviations from the square law at large d are discussed in Ref. 1. Figure 2 together with Eq. (2) of Ref. 1 yields for the rigidity of wall alignment C < 1 1 0 4 erg c m 2 if we take for K33 the value used in the present paper. elusive evidence f o r liquid-crystalline curvature electricity and a ...

We describe geometric realizations for various classes of admissible representations of reductive Lie groups. The representations occur on partially holomorphic cohomology spaces corresponding to partially holomorphic homogeneous vector bundles over real group orbits in complex flag manifolds. The representations in question include standard tempered and limits of standard tempered representati...

here, the concept of quantum potential that has been illustrated in extended phase space (eps) in previous works is explored for its marginal behavior. unlike in configuration space, different representations of the quantum mechanics can be found in eps when exploiting appropriate canonical transformations. these canonical transformations revealed that there exist several representations in whi...

We describe a sensitive technique for measuring nonlinear refraction in a variety of materials that offers simplicity, sensitivity and speed. The transmittance of a sample is measured through a finite aperture in the far -field as the sample is moved along the propagation path (z) of a focused Gaussian beam. The sign and magnitude of the nonlinearity is easily deduced from such a transmittance ...