We give a complete description of the discrete spectra in branching law $\Pi|_{G'}$ with respect to pair $(G,G')=(O(p,q), O(p',q') \times O(p'',q''))$ for irreducible unitary representations $\Pi$ $G$ that are "geometric quantization" minimal elliptic coadjoint orbits. also construct explicitly all holographic operators and prove closed Parseval-type formula.

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert Communicated by Qiyu Sun. P.G.C. and A.H. were supported by NSF DMS 0704216. G.K. would like to thank the Department of Statistics at Stanford University and the Mathematics Depar...

Contrary to the simple structure of tensor product quaternionic Hilbert space, octonionic situation becomes more involved. It turns out that an space can be decomposed as orthogonal direct sum two subspaces, each them isomorphic a irreducible with real space. As application, we find for given basis, Parseval equality holds if and only basis is weak associative. Fortunately, there always exists ...

In H.264 video coding, the effect of the rate-distortion optimization (RDO) on compression efficiency increases while its complexity accounts for an important part of the computation burden. Discrete cosine transform (DCT) is one of the main operations performed as a part of the RDO operation. Therefore, the elimination of DCT operations may lead to a significant reduction of the computational ...

Decomposition in a basis: (b j) j∈J basis of L 2 ([0, 1]). ∀f ∈ L 2 ([0, 1], f = j∈J f, b j b j with f, b j = 1 0 f (t)b j (t)dt. The Parseval-Bessel norm energy conservation equality yields f 2 = j∈J |f, b j | 2 1.2 Linear and non linear approximation For any I ∈ P(J), one defines f |I by f |I = j∈I f, b j b j. The question is now how to select " a good subset " of a given size M. A first poss...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

in this paper, g-dual function-valued frames in l2(0;1) are in-troduced. we can achieve more reconstruction formulas to ob-tain signals in l2(0;1) by applying g-dual function-valued framesin l2(0;1).

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...