On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures
Fatemeh
Esmaeelzadeh
Department of Mathematics‎, ‎Bojnourd Branch‎, ‎Islamic Azad University‎, ‎Bojnourd‎, ‎Iran
author
Rajab Ali
Kamyabi-Gol
Department of Mathematics‎, ‎Center of Excellency in Analysis on Algebraic Structures(CEAAS)‎, ‎Ferdowsi University Of Mashhad‎, Iran
author
Reihaneh
Raisi Tousi
‎Ferdowsi University Of Mashhad
author
text
article
2017
eng
In the present paper, we introduce the two-wavelet localization operator for the square integrable representation of a homogeneous space with respect to a relatively invariant measure. We show that it is a bounded linear operator. We investigate some properties of the two-wavelet localization operator and show that it is a compact operator and is contained in a Schatten $p$-class.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
4
v.
2
no.
2017
1
12
http://wala.vru.ac.ir/article_29395_ef5554cee1c1583c3bc9f17d5bb7d85c.pdf
dx.doi.org/10.22072/wala.2017.61228.1109
Characterizing sub-topical functions
Hassan
Bakhtiari
Shahid Bahonar University of Kerman
author
Hossein
Mohebi
Shahid Bahonar University of Kerman
author
text
article
2017
eng
In this paper, we first give a characterization of sub-topical functions with respect to their lower level sets and epigraph. Next, by using two different classes of elementary functions, we present a characterization of sub-topical functions with respect to their polar functions, and investigate the relation between polar functions and support sets of this class of functions. Finally, we obtain more results on the polar of sub-topical functions.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
4
v.
2
no.
2017
13
23
http://wala.vru.ac.ir/article_29393_0ee808b7959b2874e9dabf0d4972296f.pdf
dx.doi.org/10.22072/wala.2017.61257.1110
Linear preservers of Miranda-Thompson majorization on MM;N
Ahmad
Mohammadhasani
Department of Mathematics, Sirjan University of technology, Sirjan, Iran
author
Asma
Ilkhanizadeh Manesh
Vali-e-Asr University of Rafsanjan
author
text
article
2017
eng
Miranda-Thompson majorization is a group-induced cone ordering on $\mathbb{R}^{n}$ induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For $X$, $Y\in M_{m,n}$, $X$ is said to be Miranda-Thompson majorized by $Y$ (denoted by $X\prec_{mt}Y$) if there exists some $D\in \rm{Conv(G)}$ such that $X=DY$. Also, we characterize linear preservers of this concept on $M_{m,n}$.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
4
v.
2
no.
2017
25
32
http://wala.vru.ac.ir/article_29392_451002d1ba46987bb96f23d9a78e8e6a.pdf
dx.doi.org/10.22072/wala.2017.61736.1113
Wilson wavelets for solving nonlinear stochastic integral equations
Bibi Khadijeh
Mousavi
Department of Pure Mathematica, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
author
Ataollah
Askari Hemmat
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman
author
Mohammad Hossien
Heydari
Shiraz University of Technology, Shiraz,
author
text
article
2017
eng
A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It\^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It\^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operational matrices of integration and stochastic integration, the problem under study is transformed to a system of nonlinear algebraic equations which can be simply solved to obtain an approximate solution for the main problem. Moreover, a new technique for computing nonlinear terms in such problems is presented. Furthermore, convergence of Wilson wavelets expansion is investigated. Several examples are presented to show the efficiency and accuracy of the proposed method.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
4
v.
2
no.
2017
33
48
http://wala.vru.ac.ir/article_29388_cab6f5111dc82287318b83ae253c9278.pdf
dx.doi.org/10.22072/wala.2017.59458.1106
Some results on Haar wavelets matrix through linear algebra
Siddu
Shiralasetti
Pavate nagar
author
Kumbinarasaiah
S
Pavate nagar
author
text
article
2017
eng
Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
4
v.
2
no.
2017
49
59
http://wala.vru.ac.ir/article_29498_344e26e2a5021349b589b01c71d47239.pdf
dx.doi.org/10.22072/wala.2018.53432.1093
Projection Inequalities and Their Linear Preservers
Mina
Jamshidi
Graduate University of Advanced Technology, Kerman, Iran.
author
Farzad
Fatehi
University of Sussex, Brighton, United Kingdom.
author
text
article
2017
eng
This paper introduces an inequality on vectors in $\mathbb{R}^n$ which compares vectors in $\mathbb{R}^n$ based on the $p$-norm of their projections on $\mathbb{R}^k$ ($k\leq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $\sum_{i=1}^k\vert x_i\vert^p$ is less than or equal to $ \sum_{i=1}^k\vert y_i\vert^p$, for every $d\leq k\leq n$. For a relation $\sim$ on a set $X$, we say a map $f:X \rightarrow X$ is a preserver of that relation, if $x\sim y$ implies $f(x)\sim f(y)$, for every $x,y\in X$. All the linear maps that preserve $d$-projectional equality and inequality are characterized in this paper.
Wavelet and Linear Algebra
Vali-e-Asr university of Rafsanjan
2383-1936
4
v.
2
no.
2017
61
67
http://wala.vru.ac.ir/article_29391_0c3c85a7a89bc6f8ac60bfcc89b198b0.pdf
dx.doi.org/10.22072/wala.2017.63024.1115