Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
1
2018
08
01
On a New G-Frame and Duality
1
9
EN
Reihaneh
Raisi Tousi
Ferdowsi University of Mashhad
raisi@um.ac.ir
Rajab Ali
Kamyabi Gol
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775,
Mashhad, Iran.
kamyabi@um.ac.ir
Hosein
Avazzadeh
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775,
Mashhad, Iran.
avazzadeh@gmail.com
10.22072/wala.2017.51870.1089
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.<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.
Singleton g-frame operator,Dual of a singleton g-frame,Singleton g-Riesz basis,Singleton g-orthonormal basis
http://wala.vru.ac.ir/article_26091.html
http://wala.vru.ac.ir/article_26091_28688f4eb210f2627bfedfc3f1f7ebd4.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
1
2018
08
01
A Necessary Condition for a Shearlet System to be a Frame via Admissibility
11
26
EN
Mojgan
Aminkhah
Department of Applied Mathematics, Faculty of Sciences and new Technologies,
Graduate University of Advanced Technology, P. O. Box 76315-115, Kerman, Iran.
m.aminkhah@student.kgut.ac.ir
Ataollah
Askari Hemmat
Shahid Bahonar University of Kerman
askari@uk.ac.ir
Reihaneh
Raisi Tousi
Ferdowsi University of Mashhad
raisi@um.ac.ir
10.22072/wala.2017.59948.1105
Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.
Shearlet system,Cone-adapted shearlet system,Shearlet frame,Admissibility condition
http://wala.vru.ac.ir/article_26093.html
http://wala.vru.ac.ir/article_26093_1c44ed44bbe35144754ecb1a18a258e0.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
1
2018
08
01
Banach Pair Frames
27
47
EN
Abolhassan
Fereydooni
Department of Basic Sciences, Ilam University, Ilam, Iran
fereydooniman@yahoo.com
Ahmad
Safapour
Vali-e-Asr university
safapour@vru.ac.ir
10.22072/wala.2017.60236.1107
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 $ell$. <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.
Banach frame,Atomic decomposition,(Banach)pair frame,(Banach)pair Bessel
http://wala.vru.ac.ir/article_26094.html
http://wala.vru.ac.ir/article_26094_0c0d148484fcc5a150633b2e99bc2cc9.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
1
2018
08
01
Some Results on Convex Spectral Functions: I
49
56
EN
Ali Reza
Sattarzadeh
Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran.
arsattarzadeh@gmail.com
Hossein
Mohebi
Shahid Bahonar University of Kerman
hmohebi@uk.ac.ir
10.22072/wala.2017.66630.1123
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.
Spectral function,Proximal average,Moreau envelope,Infimal convolution
http://wala.vru.ac.ir/article_29390.html
http://wala.vru.ac.ir/article_29390_8fbfacedf5f697bbe26f048cf0b44053.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
1
2018
08
01
p-adic Shearlets
57
71
EN
Mahdieh
Fatemidokht
Depatrment of pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
fatemidokht@gmail.com
Ataollah
Askari Hemmat
Depatrment of Mathematics Graduate University of Advanced Technology
askarihemmat@gmail.com
10.22072/wala.2017.61717.1112
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.
Fourier transform,continuous p-adic shearlet transform,p-adic shearlet system
http://wala.vru.ac.ir/article_29394.html
http://wala.vru.ac.ir/article_29394_53c2ff2b53834194d66fb0fe56531761.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
5
1
2018
08
01
The Sign-Real Spectral Radius for Real Tensors
73
87
EN
Hamid Reza
Afshin
Vali-e-Asr University of Rafsanjan
hamidrezaafshin@yahoo.com
Ali Reza
Shojaeifard
Department of Mathematics, Faculty of Sciences, Imam Hossein
Comprehensive University, Tehran, Islamic Republic of Iran
ashojaeifard@ihu.ac.ir
10.22072/wala.2018.71992.1134
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.
Higher order tensor,Nonnegative tensor,Perron Frobenius theorem
http://wala.vru.ac.ir/article_31755.html
http://wala.vru.ac.ir/article_31755_fdd95296e0cd5cd23bf0aa5f70fe3882.pdf