2020-12-02T07:12:08Z
http://wala.vru.ac.ir/?_action=export&rf=summon&issue=5141
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2018
5
1
On a New G-Frame and Duality
Reihaneh
Raisi Tousi
Rajab Ali
Kamyabi Gol
Hosein
Avazzadeh
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.
Singleton g-frame operator
Dual of a singleton g-frame
Singleton g-Riesz basis
Singleton g-orthonormal basis
2018
06
01
1
9
http://wala.vru.ac.ir/article_26091_28688f4eb210f2627bfedfc3f1f7ebd4.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2018
5
1
A Necessary Condition for a Shearlet System to be a Frame via Admissibility
Mojgan
Aminkhah
Ataollah
Askari Hemmat
Reihaneh
Raisi Tousi
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
2018
06
01
11
26
http://wala.vru.ac.ir/article_26093_1c44ed44bbe35144754ecb1a18a258e0.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2018
5
1
Banach Pair Frames
Abolhassan
Fereydooni
Ahmad
Safapour
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.
Banach frame
Atomic decomposition
(Banach)pair frame
(Banach)pair Bessel
2018
06
01
27
47
http://wala.vru.ac.ir/article_26094_0c0d148484fcc5a150633b2e99bc2cc9.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2018
5
1
Some Results on Convex Spectral Functions: I
Ali Reza
Sattarzadeh
Hossein
Mohebi
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
2018
06
01
49
56
http://wala.vru.ac.ir/article_29390_8fbfacedf5f697bbe26f048cf0b44053.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2018
5
1
p-adic Shearlets
Mahdieh
Fatemidokht
Ataollah
Askari Hemmat
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
2018
06
01
57
71
http://wala.vru.ac.ir/article_29394_53c2ff2b53834194d66fb0fe56531761.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2018
5
1
The Sign-Real Spectral Radius for Real Tensors
Hamid Reza
Afshin
Ali Reza
Shojaeifard
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
2018
06
01
73
87
http://wala.vru.ac.ir/article_31755_fdd95296e0cd5cd23bf0aa5f70fe3882.pdf