An introductory theory of frames on finite dimensional left quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

Analytical extensions and resulting Penrose diagrams are given for the solutions of a simple 2d dilaton gravity theory describing black holes which are static as viewed by asymptotically accelerated observers.

An affine-group-based design methodology of Gabor-type filter bank is presented for the purpose of image analysis and synthesis. Various tessellations of the combined spatial-feature space are considered. We combine ideas introduced by Daugman [J.G. Daugman, Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters, J. ...

By considering charged black hole solutions of a one parameter family of two dimensional dilaton gravity theories, one finds the existence of quantum mechanically stable gravitational kinks with a simple mass to charge relation. Unlike their Einsteinian counterpart (i.e. extreme ReissnerNordström), these have nonvanishing horizon surface gravity.

Frames are constructed on the unit ball Bd in Rd consisting of smooth functions with small shrinking supports. The new frames are designed so that they can be used for decomposition of weighted Triebel Lizorkin and Besov spaces on Bd with weight wμ(x) := (1 − |x|2)μ−1/2, μ half integer, μ ≥ 0.

Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion fram...

We show that the principal block O0 of the BGG category O for a semisimple Lie algebra g acts faithfully on itself via exact endofunctors which preserve tilting modules, via right exact endofunctors which preserve projective modules and via left exact endofunctors which preserve injective modules. The origin of all these functors is tensoring with arbitrary (not necessarily finite-dimensional) ...

The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the c...

In this article, we consider pair frames in Banach spaces and   introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as   special kinds of (Banach) pair frames.  Some frame-like inequalities  for (Banach)  pair frames are presented. The elements that participant  in the construction of (Ba...