Quaternionic Hilbert spaces play an important role in applied physical sciences especially quantum physics. In this paper, the operator valued frames on quaternionic are introduced and studied. terms of a class partial isometries spaces, parametrization Parseval is obtained. We extend to many properties vector process. Moreover, we show that all can be obtained from single frame. Finally, sever...

The problem of representation and analysis of functions defined on manifolds (signals, images, and data in general) is ubiquities in many fields ranging from statistics and cosmology to neuroscience and biology. It is very common to consider input signals as points in a high-dimensional measurement space, however, meaningful structures lay on a manifold embedded in this space. In the last decad...

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.

In this series of lectures the basic ideas of the 1=m Q expansion in QCD (m Q is the mass of a heavy quark) are outlined. Applications to exclusive and inclusive decays are given.

I examine how firms use alliances to respond to the alliance networks of their rivals, by either allying with their rivals’ partners or by building countervailing alliances. Evidence from the global airline industry (1994–98) suggests that these strategic responses depend on alliance cospecialization. Cospecialized alliances by rivals may involve exclusivity, precluding alliances with the rival...

We investigated the drawing signs in 200 schizophrenic and 200 normal individuals on Draw A Person test in Pakistan. The sample consisted of men and women between ages of 20 to 50 years in two provinces (Punjab and Khyber Pakhtun-Khwa) of Pakistan. We used Koppitz (1971) method to administer and score the test and selected 40 Emotional Indicators (EIs) from the literature and found 26whichsigni...