WAVELET AND LINEAR ALGEBRA
Year:2018 | Volume:5 | Issue:1|Papers Count:6

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames. Also, we investigate duality for some kinds of g-frames. Finally, we illustrate an example which provides a suitable translation from discrete frames to Sun’ s gframes.

Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.

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 (Banach) pair frames are characterized. It is shown that a Banach space X has a Banach pair frame with respect to a Banach scalar sequence space `, when it is precisely isomorphic to a complemented subspace of `. It is shown that if we are allowed to choose the scalar sequence space, pair frames and Banach pair frames with respect to the chosen scalar sequence space denote the same concept.

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infi mal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-defi nite programmings and engineering problems.

The fi eld Qp of p-adic numbers is defi ned as the completion of the fi eld of the rational numbers Q with respect to the p-adic norm j: jp. In this paper, we study the continuous and discrete padic shearlet systems on L 2 (Q 2 p). We also suggest discrete padic shearlet frames. Several examples are provided.

In this paper a new quantity for real tensors, the sign-real spectral radius, is defi ned and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.