Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2
1
2015
09
01
On the characterization of subrepresentations of shearlet group
1
9
EN
V.
Atayi
Department of Pure Mathematics, Ferdowsi University of Mashhad,
Mashhad, Islamic Republic of Iran
R. A.
Kamyabi-Gol
Department of Pure Mathematics, Ferdowsi University of Mashhad,
Mashhad, Islamic Republic of Iran
We regard the shearlet group as a semidirect product group and show that its standard representation is,typically, a quasiregu- lar representation. As a result we can characterize irreducible as well as square-integrable subrepresentations of the shearlet group.
Shearlet group,Semidirect product
http://wala.vru.ac.ir/article_14265.html
http://wala.vru.ac.ir/article_14265_9bf627ecedb9c35cc07168835acddb42.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2
1
2015
09
01
Cyclic wavelet systems in prime dimensional linear vector spaces
11
24
EN
A.
Ghaani Farashahi
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics,
University of Vienna
Finite affine groups are given by groups of translations and di- lations on ﬁnite cyclic groups. For cyclic groups of prime order we develop a time-scale (wavelet) analysis and show that for a large class of non-zero window signals/vectors, the generated full cyclic wavelet system constitutes a frame whose canonical dual is a cyclic wavelet frame.
Cyclic wavelet system,Cyclic wavelet frame
http://wala.vru.ac.ir/article_14266.html
http://wala.vru.ac.ir/article_14266_785b6fb99f7fe9032e4a04c9dc31a079.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2
1
2015
09
01
On the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues
25
38
EN
E.
Kokabifar
Faculty of Science, Yazd University, Yazd, Islamic Republic of Iran.
G.B.
Loghmani
Faculty of Science, Yazd University, Yazd, Islamic Republic of Iran.
A. M.
Nazari
Department of Mathematics, Faculty of Science, Arak University, Arak,
Islamic Republic of Iran.
S. M.
Karbassi
Department of Mathematics, Yazd Branch, Islamic Azad University, Yazd,
Islamic Republic of Iran.
Consider an n × n matrix polynomial P(λ). A spectral norm distance from P(λ) to the set of n × n matrix polynomials that have a given scalar µ ∈ C as a multiple eigenvalue was introduced and obtained by Papathanasiou and Psarrakos. They computed lower and upper bounds for this distance, constructing an associated perturbation of P(λ). In this paper, we extend this result to the case of two given distinct complex numbers µ1 and µ2. First, we compute a lower bound for the spectral norm distance from P(λ) to the set of matrix polynomials that have µ1, µ2 as two eigenvalues. Then we construct an associated perturbation of P(λ) such that the perturbed matrix polynomial has two given scalars µ1 and µ2 in its spectrum. Finally, we derive an upper bound for the distance by the constructed perturbation of P(λ). Numerical examples are provided to illustrate the validity of the method.
Matrix polynomial,Eigenvalue,Perturbation,Singular value
http://wala.vru.ac.ir/article_14267.html
http://wala.vru.ac.ir/article_14267_031c86cfbf3947aad1230b028a5506b5.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2
1
2015
09
01
G-dual function-valued frames in L2(0,∞)
39
47
EN
M. A.
Hasankhanifard
Vali-e-Asr university of Rafsanjan
M. A.
Dehghan
Vali-e-Asr university of Rafsanjan
In this paper, g-dual function-valued frames in L2(0;1) are in- troduced. We can achieve more reconstruction formulas to ob- tain signals in L2(0;1) by applying g-dual function-valued frames in L2(0;1).
g-dual frame,function-valued frame
http://wala.vru.ac.ir/article_14268.html
http://wala.vru.ac.ir/article_14268_9b2b81f3b7b0c0ef1d67b31101cdd174.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2
1
2015
09
01
Schur multiplier norm of product of matrices
49
54
EN
M.
Khosravi
Shahid Bahonar university of Kerman
A.
Sheikhhosseini
Shahid Bahonar university of Kerman
For A ∈ M n, the Schur multiplier of A is defined as S A(X) = A ◦ X for all X ∈ M n and the spectral norm of S A can be state as ∥S A∥ = supX,0 ∥A ∥X ◦X ∥ ∥. The other norm on S A can be defined as ∥S A∥ω = supX,0 ω(ω S( AX (X ) )) = supX,0 ωω (A (X ◦X ) ), where ω(A) stands for the numerical radius of A. In this paper, we focus on the relation between the norm of Schur multiplier of product of matrices and the product of norm of those matrices. This relation is proved for Schur product and geometric product and some applications are given. Also we show that there is no such relation for operator product of matrices. Furthermore, for positive definite matrices A and B with ∥S A∥ω ⩽ 1 and ∥S B∥ω ⩽ 1, we show that A♯B = n(I − Z)1/2C(I + Z)1/2, for some contraction C and Hermitian contraction Z.
Schur multiplier,Schur product,Geometric product,Positive semideﬁnite
matrix,Numerical radius
http://wala.vru.ac.ir/article_14269.html
http://wala.vru.ac.ir/article_14269_e9a1dc6d7c67b98d454cd7225318629e.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2
1
2015
09
01
Ultra Bessel sequences in direct sums of Hilbert spaces
55
64
EN
M. R.
Abdollahpour
University
of Mohaghegh Ardabili
A.
Rahimi
University of Maragheh
In this paper, we establish some new results in ultra Bessel sequences and ultra Bessel sequences of subspaces. Also, we investigate ultra Bessel sequences in direct sums of Hilbert spaces. Specially, we show that {( fi, gi)}∞ i=1 is a an ultra Bessel sequence for Hilbert space H ⊕ K if and only if { fi}∞ i=1 and {gi}∞ i=1 are ultra Bessel sequences for Hilbert spaces H and K, respectively.
Frame of subspaces,Ultra Bessel sequence
http://wala.vru.ac.ir/article_14270.html
http://wala.vru.ac.ir/article_14270_489abf58eb663e969ea22c4d90360acb.pdf
Vali-e-Asr university of Rafsanjan
Wavelet and Linear Algebra
2383-1936
2476-3926
2
1
2015
09
01
Some relations between ε-directional derivative and ε-generalized weak subdifferential
65
80
EN
A.
Mohebi
Shahid Bahonar university of Kerman
H.
Mohebi
Shahid Bahonar university of Kerman
In this paper, we study ε-generalized weak subdifferential for vector valued functions defined on a real ordered topological vector space X. We give various characterizations of ε-generalized weak subdifferential for this class of functions. It is well known that if the function f : X → R is subdifferentiable at x0 ∈ X, then f has a global minimizer at x0 if and only if 0 ∈ ∂ f(x0). We show that a similar result can be obtained for ε-generalized weak subdifferential. Finally, we investigate some relations between ε-directional derivative and ε-generalized weak subdifferential. In fact, in the classical subdifferential theory, it is well known that if the function f : X → R is subdifferentiable at x0 ∈ X and it has directional derivative at x0 in the direction u ∈ X, then the relation f ′(x0, u) ≥ ⟨u, x∗⟩, ∀ x∗ ∈ ∂ f(x0) is satisfied. We prove that a similar result can be obtained for ε- generalized weak subdifferential.
Non-convex optimization,"-directional derivative
http://wala.vru.ac.ir/article_14591.html
http://wala.vru.ac.ir/article_14591_7255b9cf0db6154ec39af397e9141d48.pdf