Frames have turned out to be an essential tool for many applications such as, for example, data transmission, due to their robustness not only against noise but also against losses and due to their freedom in design [4, 6]. Their main advantage lies in the fact that a frame can be designed to be redundant while still providing a reconstruction formula. Since the frame operator Sg = ∑n i=1 〈g, f...

Functional Gabor single-frame or multi-frame generator multipliers are the matrices of function entries that preserve Parseval generators. An interesting and natural question is how to characterize all such multipliers. This has been answered for several special cases including case generators in two dimensions one-dimension. In this paper we completely with respect separable time-frequency lat...

Abstract In this paper, we introduce the two-sided fractional quaternion Fourier transform (FrQFT) and give some properties of it. The main results paper are divided into three parts. Firstly a definition FrQFT. Secondly based on QFT, study relationship between QFT FrQFT, differential FrQFT Parseval identity. Finally, an example to illustrate application its inverse in solving partial equations.

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.

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.

The shearlet representation has gained increasing recognition in recent years as a framework for the efficient representation of multidimensional data. This representation consists of a countable collection of functions defined at various locations, scales and orientations, where the orientations are obtained through the use of shearing matrices. While shearing matrices offer the advantage of p...

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 ...