Wavelet and Linear AlgebraWavelet and Linear Algebra
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Sun, 25 Jun 2017 23:24:48 +0100FeedCreatorWavelet and Linear Algebra
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Feed provided by Wavelet and Linear Algebra. Click to visit.Classical wavelet systems over finite fields
http://wala.vru.ac.ir/article_23236_3343.html
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.Wed, 30 Nov 2016 20:30:00 +0100Linear combinations of wave packet frames for L^2(R^d)
http://wala.vru.ac.ir/article_23237_3343.html
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.Wed, 30 Nov 2016 20:30:00 +0100Characterizations of amenable hypergroups
http://wala.vru.ac.ir/article_23365_0.html
Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.Sat, 31 Dec 2016 20:30:00 +0100Cartesian decomposition of matrices and some norm inequalities
http://wala.vru.ac.ir/article_23238_3343.html
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.Wed, 30 Nov 2016 20:30:00 +0100Determination of subrepresentations of the standard higher dimensional shearlet group
http://wala.vru.ac.ir/article_23366_0.html
‎This paper is devoted to definition standard higher dimension shearlet group $ mathbb{S} = mathbb{R}^{+} times mathbb {R}^{n-1} times mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group‎. ‎Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations‎.Sat, 31 Dec 2016 20:30:00 +0100Pseudoframe multiresolution structure on abelian locally compact groups
http://wala.vru.ac.ir/article_23239_3343.html
‎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.Wed, 30 Nov 2016 20:30:00 +0100On higher rank numerical hulls of normal matrices
http://wala.vru.ac.ir/article_23367_0.html
‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1$ and $A_2$ are Hermitian‎, ‎are investigated‎. ‎The higher rank numerical hulls of the basic circulant matrix‎ ‎are also studied‎.Sat, 31 Dec 2016 20:30:00 +0100Quartic and pantic B-spline operational matrix of fractional integration
http://wala.vru.ac.ir/article_23240_3343.html
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.Wed, 30 Nov 2016 20:30:00 +0100A-B-imprimitivity bimodule frames
http://wala.vru.ac.ir/article_25011_0.html
Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the last part of the paper investigates dual of an A-frame and a B-frame and presents a common property for all duals of a frame in a Hilbert A-B-imprimitivity bimodule.Wed, 12 Apr 2017 19:30:00 +0100Triangularization over finite-dimensional division rings using the reduced trace
http://wala.vru.ac.ir/article_23241_3343.html
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.Wed, 30 Nov 2016 20:30:00 +0100Some results on the block numerical range
http://wala.vru.ac.ir/article_25012_0.html
The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.Wed, 12 Apr 2017 19:30:00 +0100On a new G-frame and duality
http://wala.vru.ac.ir/article_26091_0.html
In this note we introduce a new (singleton) g-frame, g-orthonormal and g-Riesz bases and compare them with the corresponding notions in [14] and [1]. Also, we continue our research on frame operator of a g-frame and obtain a relation between Sun [14] and Ali et al. [1] frame operators. Then we study duality in g-frames and establish relations between dual of g-frames and dual of continuous frames. Finally, we illustrate an example which provides a suitable translation from discrete frames to Sun's g-frames.Fri, 23 Jun 2017 19:30:00 +0100Wavelet-based numerical method for solving fractional integro-differential ...
http://wala.vru.ac.ir/article_26092_0.html
This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented for driving approximate solution FIDEs with a weakly singular kernel‎. ‎Error estimates of all proposed numerical methods are given to test the convergence and accuracy of the method‎. ‎A comparative study of accuracy and computational time for the presented techniques is given‎.Fri, 23 Jun 2017 19:30:00 +0100A necessary condition for a Shearlet system to be a frame via admissibility
http://wala.vru.ac.ir/article_26093_0.html
Necessary conditions for shearlet and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of genera- tors. Discrete and cone-adapted discrete shearlet systems are studied by Kutyniok and Labate in [11, 13]. They have derived sufficient conditions in [11] for a discrete shearlet system to form a frame for L2(R2) We provide a relation between shearlet frames and admissibility condition of the generators.Fri, 23 Jun 2017 19:30:00 +0100Banach Pair Frames
http://wala.vru.ac.ir/article_26094_0.html
In this article, we consider pair frames in Banach spaces and introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as special kinds of (Banach) pair frames. Some frame-like inequalities for (Banach) pair frames are presented. The elements that participant in the construction of (Banach) pair frames are characterized. It is shown that a Banach space X has a Banach pair frame with respect to a Banach scalar sequence space l, when it is precisely isomorphic to a complemented subspace of l. It is shown that if we are allowed to choose the scalar sequence space, pair frames and Banach pair frames with respect to the chosen scalar sequence space denote the same concept.Fri, 23 Jun 2017 19:30:00 +0100