On intertwining dilations

Paschke Dilations

Intertwining Operators between Line Bundles on Grassmannians

Let G = GL(n, F ) where F is a local field of arbitrary characteristic, and let π1, π2 be representations induced from characters of two maximal parabolic subgroups P1, P2. We explicitly determine the space HomG (π1, π2) of intertwining operators and prove that it has dimension ≤ 1 in all cases.

On Affine Frames with Transcendental Dilations

We answer a question of O. Christensen about affine systems in L2(R). Specifically, we show that if the dilation factor a > 1 is transcendental, then cancellations cannot occur between different scales, in the conditions for the affine system to form a frame. Such cancellations are known to occur when a is an integer.

Dilations Preserving a Bound on The

The probl(~~n is t.o choose t.he missing en·try .in the opera·tor-Dm.at.ri:g: rA tB so a.s. to sat:isfy a bound on the norm,. 1\SO\V for c)" / D li ;;, p it is obviou.sly necessary tha·t :£ ]1 and IICA Clli ::> P" Is t.his pair of n.ecessa:r.y condi·tions also sufficient? One is led t.o doubt~ i·t if one has·tily p:c,2Sl.U118S that the choice D = 0 is norm,=mi.nimizing., P1l though il (1 1) II ...

On decoding procedures of intertwining codes

One of the main weakness of the family of centralizer codes is that its length is always n. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form nk. We establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. We also show an inclusion of linear codes into a specia...