On a New G-Frame and Duality
Reihaneh
Raisi Tousi
Ferdowsi University of Mashhad
author
Rajab Ali
Kamyabi Gol
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775,
Mashhad, Iran.
author
Hosein
Avazzadeh
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775,
Mashhad, Iran.
author
text
article
2018
eng
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 g-frames.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
5
v.
1
no.
2018
1
9
http://wala.vru.ac.ir/article_26091_28688f4eb210f2627bfedfc3f1f7ebd4.pdf
dx.doi.org/10.22072/wala.2017.51870.1089
A Necessary Condition for a Shearlet System to be a Frame via Admissibility
Mojgan
Aminkhah
Department of Applied Mathematics, Faculty of Sciences and new Technologies,
Graduate University of Advanced Technology, P. O. Box 76315-115, Kerman, Iran.
author
Ataollah
Askari Hemmat
Shahid Bahonar University of Kerman
author
Reihaneh
Raisi Tousi
Ferdowsi University of Mashhad
author
text
article
2018
eng
Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
5
v.
1
no.
2018
11
26
http://wala.vru.ac.ir/article_26093_1c44ed44bbe35144754ecb1a18a258e0.pdf
dx.doi.org/10.22072/wala.2017.59948.1105
Banach Pair Frames
Abolhassan
Fereydooni
Department of Basic Sciences, Ilam University, Ilam, Iran
author
Ahmad
Safapour
Vali-e-Asr university
author
text
article
2018
eng
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 $\mathrm{X}$ has a Banach pair frame with respect to a Banach scalar sequence space $\ell$, when it is precisely isomorphic to a complemented subspace of $\ell$. 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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
5
v.
1
no.
2018
27
47
http://wala.vru.ac.ir/article_26094_0c0d148484fcc5a150633b2e99bc2cc9.pdf
dx.doi.org/10.22072/wala.2017.60236.1107
Some Results on Convex Spectral Functions: I
Ali Reza
Sattarzadeh
Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran.
author
Hossein
Mohebi
Shahid Bahonar University of Kerman
author
text
article
2018
eng
In 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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
5
v.
1
no.
2018
49
56
http://wala.vru.ac.ir/article_29390_8fbfacedf5f697bbe26f048cf0b44053.pdf
dx.doi.org/10.22072/wala.2017.66630.1123
p-adic Shearlets
Mahdieh
Fatemidokht
Depatrment of pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
author
Ataollah
Askari Hemmat
Depatrment of Mathematics Graduate University of Advanced Technology
author
text
article
2018
eng
The 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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
5
v.
1
no.
2018
57
71
http://wala.vru.ac.ir/article_29394_53c2ff2b53834194d66fb0fe56531761.pdf
dx.doi.org/10.22072/wala.2017.61717.1112
The Sign-Real Spectral Radius for Real Tensors
Hamid Reza
Afshin
Vali-e-Asr University of Rafsanjan
author
Ali Reza
Shojaeifard
Department of Mathematics, Faculty of Sciences, Imam Hossein
Comprehensive University, Tehran, Islamic Republic of Iran
author
text
article
2018
eng
In 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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
5
v.
1
no.
2018
73
87
http://wala.vru.ac.ir/article_31755_fdd95296e0cd5cd23bf0aa5f70fe3882.pdf
dx.doi.org/10.22072/wala.2018.71992.1134