If [GAMMA] acts on a

homogeneous space G/H properly discontinuously and freely, then the double coset space [GAMMA]\G/H has a natural manifold structure.

For now, we leave the environment unspecified, but in the calculations, it will be either a

homogeneous space or a conducting cylinder.

K could be a

homogeneous space or a space of constant curvature.

(X, d, [mu]) is said to be a

homogeneous space. Let 0 [less than or equal to] [lambda] [less than or equal to] [infinity], 0 [less than or equal to] l < 1, 1 < [q.sub.1] < 1/, 1/[q.sub.2] = 1/[q.sub.1] - 1, [lambda] - 1/[q.sub.2] < [alpha] < [lambda] + 1 - 1/[q.sub.1], and 0 < [p.sub.1] [less than or equal to] [p.sub.2] < [infinity], if a sublinear operator [T.sub.l] meets the following requirements:

Then M can be expressed as a

homogeneous space ( G/K, g) where K is the isotropy group at a fixed point o of M, and g is a G-invariant metric.

Hence we obtain the dS spacetime as the

homogeneous spaceLie-Yamaguti algebras were introduced by Yamaguti [1] (who formerly called them "generalized Lie triple systems") in an algebraic study of the characteristic properties of the torsion and curvature ofa

homogeneous space with canonical connection [2].

Gianazza [11] showed a reverse Holder inequality on

homogeneous spaces. Since the ball [B.sub.R]([[xi].sub.0]) which is induced by the vector fields is a

homogeneous space, it is obvious that the cylinder [Q.sub.R]([[xi].sub.0], [t.sub.0]) = [B.sub.R]([[xi].sub.0) x (t - [R.sup.2], t) is also a

homogeneous space.

1.5.2: Set of recorders are called a

homogeneous space of recorders, if all its elements equally receive all signals.

The art of perspective, as it was rediscovered by the Renaissance masters, operates with the notion of a

homogeneous space, identical to the one that modem techniques and automated projections resort to, used in the achievement of computer three-dimensional images in our times, which techniques could not have been known without the knowledge of artistic perspective.

Drawn from two January 2012 workshops, this collection reviews the history of geometric analysis on Euclidean and

homogeneous space, and presents new results in Radon transforms, Penrose transforms, representation theory, equivariant differential operators, wavelets related to symmetric cones, inductive limits of Lie groups, and noncommutative harmonic analysis.

acting in an infinite

homogeneous space with permeability The field observed in the lower half-space can be found using the image currents