Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365120180801On a New G-Frame and Duality192609110.22072/wala.2017.51870.1089ENReihaneh Raisi TousiFerdowsi University of MashhadRajab Ali Kamyabi GolDepartment of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775,
Mashhad, Iran.Hosein AvazzadehDepartment of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775,
Mashhad, Iran.Journal Article20161031We 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.<br />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 g-frames.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365120180801A Necessary Condition for a Shearlet System to be a Frame via Admissibility11262609310.22072/wala.2017.59948.1105ENMojgan AminkhahDepartment of Applied Mathematics, Faculty of Sciences and new Technologies,
Graduate University of Advanced Technology, P. O. Box 76315-115, Kerman, Iran.Ataollah Askari HemmatShahid Bahonar University of KermanReihaneh Raisi TousiFerdowsi University of MashhadJournal Article20170227 Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365120180801Banach Pair Frames27472609410.22072/wala.2017.60236.1107ENAbolhassan FereydooniDepartment of Basic Sciences, Ilam University, Ilam, IranAhmad SafapourVali-e-Asr universityJournal Article20170303In 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 $mathrm{X}$ has a Banach pair frame with respect to a Banach scalar sequence space $ell$, when it is precisely isomorphic to a complemented subspace of $ell$. <br />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.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365120180801Some Results on Convex Spectral Functions: I49562939010.22072/wala.2017.66630.1123ENAli Reza SattarzadehDepartment of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran.Hossein MohebiShahid Bahonar University of KermanJournal Article20170620In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal 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-definite programmings and engineering problems.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365120180801p-adic Shearlets57712939410.22072/wala.2017.61717.1112ENMahdieh FatemidokhtDepatrment of pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of KermanAtaollah Askari HemmatDepatrment of Mathematics Graduate University of Advanced TechnologyJournal Article20170409The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19365120180801The Sign-Real Spectral Radius for Real Tensors73873175510.22072/wala.2018.71992.1134ENHamid Reza AfshinVali-e-Asr University of RafsanjanAli Reza ShojaeifardDepartment of Mathematics, Faculty of Sciences, Imam Hossein
Comprehensive University, Tehran, Islamic Republic of IranJournal Article20171105In this paper a new quantity for real tensors, the sign-real spectral radius, is defined 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.