then the Cauchy sequence [([[~.T].sub.n]).sub.n = 1.sup.[infinity]] convergent to some linear isometry
Moreover [Mathematical Expression Omitted] is an isometry
from [Mathematical Expression Omitted] to [Mathematical Expression Omitted] and [Mathematical Expression Omitted] from [Mathematical Expression Omitted] to [Mathematical Expression Omitted].
* General relativistic theories: the isometry
We have filled out the diagonal of U to make it an isometry
Regression analysis for the log of lower leg length relative to the log of the femur length, differences respect to isometry
(slope value equal 1) and slope homogeneity test with respect to theropods.
Cartan in  showed that the examples above cover, in fact, all possible 3-dimensional homogeneous spaces with 4-dimensional isometry
Thus [mathematical expression not reproducible] Jarosz  and Jarosz and Pathak  studied ||/ ||o([0>1]).) Jarosz  and Jarosz and Pathak  studied a problem when an isometry
on a space of continuous functions is a weighted composition operator.
Let X be the Hardy space [H.sup.p] or the Bergman space [L.sup.p.sub.a] (1 < p < [infinity], p [not equal to] 2) and T = [mu][([phi]').sup.[beta]][C.sub.[phi]] be a surjective linear isometry
on X for some [phi] [member of] Aut(D) and |[mu]| = 1 where [beta] = [1/p] for the space [H.sup.p] and [beta] = [2/p] for the space [L.sup.p.suba.].If T is weakly supercyclic then [phi] is not an elliptic automorphism.
Using the isometry
property (8) of the stochastic integral and (28), we have
One of the most commonly known conditions is the restricted isometry
Since the entries of [PHI]D are correlated when D is highly coherent, [PHI]D may no longer satisfy the standard restricted isometry
property (RIP ) and the mutual incoherence property (MIP ) which are commonly used in the standard CS framework.
However, the CS-based broadband channel estimation is more complex than the SAF algorithms because the CS-based channel estimations require measurement matrix construction which is bounded by restricted isometry