eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2018-08-01
5
1
1
9
10.22072/wala.2017.51870.1089
26091
On a New G-Frame and Duality
Reihaneh Raisi Tousi
raisi@um.ac.ir
1
Rajab Ali Kamyabi Gol
kamyabi@um.ac.ir
2
Hosein Avazzadeh
avazzadeh@gmail.com
3
Ferdowsi University of Mashhad
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran.
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran.
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.
http://wala.vru.ac.ir/article_26091_28688f4eb210f2627bfedfc3f1f7ebd4.pdf
Singleton g-frame operator
Dual of a singleton g-frame
Singleton g-Riesz basis
Singleton g-orthonormal basis
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2018-08-01
5
1
11
26
10.22072/wala.2017.59948.1105
26093
A Necessary Condition for a Shearlet System to be a Frame via Admissibility
Mojgan Aminkhah
m.aminkhah@student.kgut.ac.ir
1
Ataollah Askari Hemmat
askari@uk.ac.ir
2
Reihaneh Raisi Tousi
raisi@um.ac.ir
3
Department of Applied Mathematics, Faculty of Sciences and new Technologies, Graduate University of Advanced Technology, P. O. Box 76315-115, Kerman, Iran.
Shahid Bahonar University of Kerman
Ferdowsi University of Mashhad
Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.
http://wala.vru.ac.ir/article_26093_1c44ed44bbe35144754ecb1a18a258e0.pdf
Shearlet system
Cone-adapted shearlet system
Shearlet frame
Admissibility condition
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2018-08-01
5
1
27
47
10.22072/wala.2017.60236.1107
26094
Banach Pair Frames
Abolhassan Fereydooni
fereydooniman@yahoo.com
1
Ahmad Safapour
safapour@vru.ac.ir
2
Department of Basic Sciences, Ilam University, Ilam, Iran
Vali-e-Asr university
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.
http://wala.vru.ac.ir/article_26094_0c0d148484fcc5a150633b2e99bc2cc9.pdf
Banach frame
Atomic decomposition
(Banach)pair frame
(Banach)pair Bessel
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2018-08-01
5
1
49
56
10.22072/wala.2017.66630.1123
29390
Some Results on Convex Spectral Functions: I
Ali Reza Sattarzadeh
arsattarzadeh@gmail.com
1
Hossein Mohebi
hmohebi@uk.ac.ir
2
Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran.
Shahid Bahonar University of Kerman
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.
http://wala.vru.ac.ir/article_29390_8fbfacedf5f697bbe26f048cf0b44053.pdf
Spectral function
Proximal average
Moreau envelope
Infimal convolution
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2018-08-01
5
1
57
71
10.22072/wala.2017.61717.1112
29394
p-adic Shearlets
Mahdieh Fatemidokht
fatemidokht@gmail.com
1
Ataollah Askari Hemmat
askarihemmat@gmail.com
2
Depatrment of pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
Depatrment of Mathematics Graduate University of Advanced Technology
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.
http://wala.vru.ac.ir/article_29394_53c2ff2b53834194d66fb0fe56531761.pdf
Fourier transform
continuous p-adic shearlet transform
p-adic shearlet system
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2018-08-01
5
1
73
87
10.22072/wala.2018.71992.1134
31755
The Sign-Real Spectral Radius for Real Tensors
Hamid Reza Afshin
hamidrezaafshin@yahoo.com
1
Ali Reza Shojaeifard
ashojaeifard@ihu.ac.ir
2
Vali-e-Asr University of Rafsanjan
Department of Mathematics, Faculty of Sciences, Imam Hossein Comprehensive University, Tehran, Islamic Republic of Iran
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.
http://wala.vru.ac.ir/article_31755_fdd95296e0cd5cd23bf0aa5f70fe3882.pdf
Higher order tensor
Nonnegative tensor
Perron Frobenius theorem