It is therefore possible to associate with every angle a definite length, the side of the corresponding equilateral triangle.
First, every completely positive definite "function" on a locally compact quantum group G arises as a transform of a positive functional on the universal C⁎-algebra Cu0 ˆG) of the dual quantum group.
We prove that if there exits a u(F -accessible Borel probability measure on E, then F -accessibletinuous positive definite function ϑ on E with ϑ(0) = 1, there is a σ(F′, F)-Radon proBorelity measure with the characteristic functional ϑ ∘ u.
Continuing research begun in [15] and [16], we investigate the problem of when a closed subgroup H of a nilpotent locally compact group G has the property that every continuous positive definite function on H extends to some such function on G.
Not definitive, just definite.
For, as a given walk or a given exercise on the harp cannot take any and every time, but every performance has its definite minimum time which is unsurpassable, so, one might suppose, the movement of the heaven could not be completed in any and every time.
Every event has a definite cause.
Almost every skater has a definite routine that works for him or her.
"Money is a definite concern every time I break a twenty," Mrs. Morrison said.
Every mode has a definite frequency determined by the structure of the Sun.
