Classical wavelet systems over finite fields
Arash
Ghaani Farashahi
University of Vienna
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
2
no.
2016
1
18
http://wala.vru.ac.ir/article_23236_5150e489e24248c000bc17f050d8b322.pdf
dx.doi.org/10.22072/wala.2016.23236
Linear combinations of wave packet frames for L^2(R^d)
Ashok
Sah
University of Delhi
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
2
no.
2016
19
32
http://wala.vru.ac.ir/article_23237_9748c2d52d39dc6189458e4f3a485660.pdf
dx.doi.org/10.22072/wala.2016.23237
Cartesian decomposition of matrices and some norm inequalities
Alemeh
Sheikhhosseini
Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
author
Golamreza
Aghamollaei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
2
no.
2016
33
42
http://wala.vru.ac.ir/article_23238_64b86b56682082a7a0b0f1d249c90a93.pdf
dx.doi.org/10.22072/wala.2016.23238
Pseudoframe multiresolution structure on abelian locally compact groups
Hamide
Azarmi
Ph. D. student in Ferdowsi University of Mashhad
author
Radjabali
Kamyabi Gol
Department of pure Mathematics; Ferdowsi University of Mashhad;
author
Mohammad
Janfada
Department of pure Mathematics;Ferdowsi University of Mashhad;
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
2
no.
2016
43
54
http://wala.vru.ac.ir/article_23239_9bab4fd5ee9537b7e6c4e65984d3cc78.pdf
dx.doi.org/10.22072/wala.2016.23239
Quartic and pantic B-spline operational matrix of fractional integration
Ataollah
Askari Hemmat
Depatrment of Mathematics Graduate University of Advanced Technology
author
Tahereh
Ismaeelpour
Shahid Bahonar University of Kerman
author
Habibollah
Saeedi
Shahid Bahonar University of Kerman, Kerman, Iran
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
2
no.
2016
55
68
http://wala.vru.ac.ir/article_23240_9ff0784850a6139d46d8de6393191c71.pdf
dx.doi.org/10.22072/wala.2016.23240
Triangularization over finite-dimensional division rings using the reduced trace
Hossein
Momenaee Kermani
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
author
text
article
2016
eng
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.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
3
v.
2
no.
2016
69
74
http://wala.vru.ac.ir/article_23241_1e8aafe10279931fe51e54733c2efcbc.pdf
dx.doi.org/10.22072/wala.2016.23241