Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
3
2
2016
12
01
Classical wavelet systems over finite fields
1
18
EN
Arash
Ghaani Farashahi
University of Vienna
arash.ghaani.farashahi@univie.ac.at
10.22072/wala.2016.23236
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
http://wala.vru.ac.ir/article_23236.html
http://wala.vru.ac.ir/article_23236_5150e489e24248c000bc17f050d8b322.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
3
2
2016
12
01
Linear combinations of wave packet frames for L^2(R^d)
19
32
EN
Ashok
Kumar
Sah
University of Delhi
ashokmaths2010@gmail.com
10.22072/wala.2016.23237
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
http://wala.vru.ac.ir/article_23237.html
http://wala.vru.ac.ir/article_23237_9748c2d52d39dc6189458e4f3a485660.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
3
2
2016
12
01
Cartesian decomposition of matrices and some norm inequalities
33
42
EN
Alemeh
Sheikhhosseini
Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
sheikhhosseini@uk.ac.ir
Golamreza
Aghamollaei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
aghamollaei@uk.ac.ir
10.22072/wala.2016.23238
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
http://wala.vru.ac.ir/article_23238.html
http://wala.vru.ac.ir/article_23238_64b86b56682082a7a0b0f1d249c90a93.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
3
2
2016
12
01
Pseudoframe multiresolution structure on abelian locally compact groups
43
54
EN
Hamide
Azarmi
Ph. D. student in Ferdowsi University of Mashhad
azarmi_1347@yahoo.com
Radjabali
Kamyabi Gol
Department of pure Mathematics; Ferdowsi University of Mashhad;
kamyabi@um.ac.ir
Mohammad
Janfada
Department of pure Mathematics;Ferdowsi University of Mashhad;
janfada@um.ac.ir
10.22072/wala.2016.23239
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
http://wala.vru.ac.ir/article_23239.html
http://wala.vru.ac.ir/article_23239_9bab4fd5ee9537b7e6c4e65984d3cc78.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
3
2
2016
12
01
Quartic and pantic B-spline operational matrix of fractional integration
55
68
EN
Ataollah
Askari Hemmat
Depatrment of Mathematics Graduate University of Advanced Technology
askarihemmat@gmail.com
Tahereh
Ismaeelpour
Shahid Bahonar University of Kerman
tismaeelpour@math.uk.ac.ir
Habibollah
Saeedi
Shahid Bahonar University of Kerman, Kerman, Iran
saeedi@uk.ac.ir
10.22072/wala.2016.23240
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
http://wala.vru.ac.ir/article_23240.html
http://wala.vru.ac.ir/article_23240_9ff0784850a6139d46d8de6393191c71.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
3
2
2016
12
01
Triangularization over finite-dimensional division rings using the reduced trace
69
74
EN
Hossein
Momenaee Kermani
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
momenaee@uk.ac.ir
10.22072/wala.2016.23241
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
http://wala.vru.ac.ir/article_23241.html
http://wala.vru.ac.ir/article_23241_1e8aafe10279931fe51e54733c2efcbc.pdf