eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-12-01
3
2
1
18
10.22072/wala.2016.23236
23236
Classical wavelet systems over finite fields
Arash Ghaani Farashahi
arash.ghaani.farashahi@univie.ac.at
1
University of Vienna
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.
http://wala.vru.ac.ir/article_23236_5150e489e24248c000bc17f050d8b322.pdf
Finite field
classical wavelet group
quasi-regular representation
classical wavelet systems
classical dilation operators
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-12-01
3
2
19
32
10.22072/wala.2016.23237
23237
Linear combinations of wave packet frames for L^2(R^d)
Ashok Sah
ashokmaths2010@gmail.com
1
University of Delhi
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.
http://wala.vru.ac.ir/article_23237_9748c2d52d39dc6189458e4f3a485660.pdf
Frames
Wave Packet Systems
Linear Combinations
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-12-01
3
2
33
42
10.22072/wala.2016.23238
23238
Cartesian decomposition of matrices and some norm inequalities
Alemeh Sheikhhosseini
sheikhhosseini@uk.ac.ir
1
Golamreza Aghamollaei
aghamollaei@uk.ac.ir
2
Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
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.
http://wala.vru.ac.ir/article_23238_64b86b56682082a7a0b0f1d249c90a93.pdf
joint C-numerical radius
C-spectral norm
joint spectral radius
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-12-01
3
2
43
54
10.22072/wala.2016.23239
23239
Pseudoframe multiresolution structure on abelian locally compact groups
Hamide Azarmi
azarmi_1347@yahoo.com
1
Radjabali Kamyabi Gol
kamyabi@um.ac.ir
2
Mohammad Janfada
janfada@um.ac.ir
3
Ph. D. student in Ferdowsi University of Mashhad
Department of pure Mathematics; Ferdowsi University of Mashhad;
Department of pure Mathematics;Ferdowsi University of Mashhad;
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.
http://wala.vru.ac.ir/article_23239_9bab4fd5ee9537b7e6c4e65984d3cc78.pdf
Pseudoframe
generalized multiresolution structure
locally compact group, affine pseudoframe
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-12-01
3
2
55
68
10.22072/wala.2016.23240
23240
Quartic and pantic B-spline operational matrix of fractional integration
Ataollah Askari Hemmat
askarihemmat@gmail.com
1
Tahereh Ismaeelpour
tismaeelpour@math.uk.ac.ir
2
Habibollah Saeedi
saeedi@uk.ac.ir
3
Depatrment of Mathematics Graduate University of Advanced Technology
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman, Kerman, Iran
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.
http://wala.vru.ac.ir/article_23240_9ff0784850a6139d46d8de6393191c71.pdf
B-spline
Wavelet
fractional equation
partial differential equation
Operational matrix of integration
eng
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2016-12-01
3
2
69
74
10.22072/wala.2016.23241
23241
Triangularization over finite-dimensional division rings using the reduced trace
Hossein Momenaee Kermani
momenaee@uk.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
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.
http://wala.vru.ac.ir/article_23241_1e8aafe10279931fe51e54733c2efcbc.pdf
Triangularizable
Semigroup
Irreducible
Division ring
Reduced trace