Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 3 2 2016 12 01 Classical wavelet systems over finite fields 1 18 23236 10.22072/wala.2016.23236 EN Arash Ghaani Farashahi University of Vienna Journal Article 2015 11 23 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.
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 3 2 2016 12 01 Linear combinations of wave packet frames for L^2(R^d) 19 32 23237 10.22072/wala.2016.23237 EN Ashok Kumar Sah University of Delhi Journal Article 2015 10 04 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.
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 3 2 2016 12 01 Cartesian decomposition of matrices and some norm inequalities 33 42 23238 10.22072/wala.2016.23238 EN Alemeh Sheikhhosseini Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran Golamreza Aghamollaei Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran Journal Article 2016 02 26 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.
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 3 2 2016 12 01 Pseudoframe multiresolution structure on abelian locally compact groups 43 54 23239 10.22072/wala.2016.23239 EN Hamide Azarmi Ph. D. student in Ferdowsi University of Mashhad Radjabali Kamyabi Gol Department of pure Mathematics; Ferdowsi University of Mashhad; Mohammad Janfada Department of pure Mathematics;Ferdowsi University of Mashhad; Journal Article 2015 12 31 ‎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.
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 3 2 2016 12 01 Quartic and pantic B-spline operational matrix of fractional integration 55 68 23240 10.22072/wala.2016.23240 EN Ataollah Askari Hemmat Depatrment of Mathematics Graduate University of Advanced Technology Tahereh Ismaeelpour Shahid Bahonar University of Kerman Habibollah Saeedi Shahid Bahonar University of Kerman, Kerman, Iran Journal Article 2016 05 31 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.
Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 3 2 2016 12 01 Triangularization over finite-dimensional division rings using the reduced trace 69 74 23241 10.22072/wala.2016.23241 EN Hossein Momenaee Kermani Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman Journal Article 2016 07 27 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.