2019-09-15T18:51:18Z
http://wala.vru.ac.ir/?_action=export&rf=summon&issue=3906
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
2
Classical wavelet systems over finite fields
Arash
Ghaani Farashahi
This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full wavelet frames as well, and hence each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coefficients as well.
Finite field
classical wavelet group
quasi-regular representation
classical wavelet systems
classical dilation operators
2016
12
01
1
18
http://wala.vru.ac.ir/article_23236_5150e489e24248c000bc17f050d8b322.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
2
Linear combinations of wave packet frames for L^2(R^d)
Ashok
Sah
In this paper we study necessary and sufficient conditions for some types of linear combinations of wave packet frames to be a frame for L2(Rd). Further, we illustrate our results with some examples and applications.
Frames
Wave Packet Systems
Linear Combinations
2016
12
01
19
32
http://wala.vru.ac.ir/article_23237_9748c2d52d39dc6189458e4f3a485660.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
2
Cartesian decomposition of matrices and some norm inequalities
Alemeh
Sheikhhosseini
Golamreza
Aghamollaei
Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements are studied and investigated for the joint C-numerical radius, joint spectral radius, and for the C-spectral norm of matrices.
joint C-numerical radius
C-spectral norm
joint spectral radius
2016
12
01
33
42
http://wala.vru.ac.ir/article_23238_64b86b56682082a7a0b0f1d249c90a93.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
2
Pseudoframe multiresolution structure on abelian locally compact groups
Hamide
Azarmi
Radjabali
Kamyabi Gol
Mohammad
Janfada
Let $G$ be a locally compact abelian group. The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$. Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level. Also, the construction of affine frames for $L^2(G)$ based on a GMS is presented.
Pseudoframe
generalized multiresolution structure
locally compact group, affine pseudoframe
2016
12
01
43
54
http://wala.vru.ac.ir/article_23239_9bab4fd5ee9537b7e6c4e65984d3cc78.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
2
Quartic and pantic B-spline operational matrix of fractional integration
Ataollah
Askari Hemmat
Tahereh
Ismaeelpour
Habibollah
Saeedi
In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a system of algebraic equations. Some examples are presented to show the applicability and effectivity of the technique.
B-spline
Wavelet
fractional equation
partial differential equation
Operational matrix of integration
2016
12
01
55
68
http://wala.vru.ac.ir/article_23240_9ff0784850a6139d46d8de6393191c71.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2016
3
2
Triangularization over finite-dimensional division rings using the reduced trace
Hossein
Momenaee Kermani
In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one is a generalization of a result due to Kaplansky and in the second one a triangularizability condition which is dependent on a single element is presented.
Triangularizable
Semigroup
Irreducible
Division ring
Reduced trace
2016
12
01
69
74
http://wala.vru.ac.ir/article_23241_1e8aafe10279931fe51e54733c2efcbc.pdf