فهرست مطالب

مجله موجکها و جبر خطی
سال نهم شماره 2 (Autumn and Winter 2022)

تاریخ انتشار: 1402/01/15
تعداد عناوین: 10

فارسی
English

انتخاب همه

Elementary mappings on bounded operators defined on Hilbert spaces and Fuglede-Putnam theorem related to Aluthge transforms.

Seyed Mohammad Sadegh Nabavi Sales * Pages 1-13

In this paper we consider the generalized Aluthge transform $\tilde{A}_{(f_1,f_2)}$ for a given operator $A$ defined on a Hilbert space $H$, in which $f_1$ and $f_2$ are continuous and then we investigate the well-known Fuglede Putnam theorem for the elementary mappings $\Delta$ and $\delta$. In particular, among other things, we show that if $(A,B)$ satisfies the FP property, then so does $(\tilde{A}_{(f_1,f_2)},\tilde{B}_{(g_1,g_2)})$.

Keywords: Fuglede-Putnam theorem, Generalized Aluthge transform, Closed subspace reducing an operator

Abstract View Paper Research/Original Article Original: Persian
Continuous homomorphisms of GL2(C)

Seyed Sadegh Salehi Amiri *, Alireza Khalili Asboei Pages 79-104

Let GL_2(C) be the complex general linear group of degree 2. In this paper, we characterize thegeneral form of all continuous homomorphisms of GL_2(C). These are the continuous maps φ:GL_2(C)→GL_2 (C) which satisfyφ(AB) = φ(A)φ(B) A,B∈GL_2 (C).As a result, we present the general form of all continuous automorphisms of GL2(C).

Keywords: General linear group, Continuous homomorphism, Functional equation

Abstract View Paper Research/Original Article Original: Persian
Weak phase retrieval by vectors in $\mathbb{R}^3$ and $\mathbb{R}^4$

Fateh Akrami *, Asghar Rahimi, Bayaz Daraby, MohammadAli Hasankhani Fard Pages 127-151

and $\mathbb{R}^4$. We will classify weak phase retrievable frames in $\mathbb{R}^3$ and we will show that there are not any weak phase retrievable frames in $\mathbb{R}^3$ containing any multiple of standard basis vectors. We provide numerous examples to show that our results are the best possible.

Keywords: Real Hilbert frames, Full spark frame, Phase retrieval, Weak phase retrieval, Norm retrieval

Abstract View Paper Research/Original Article Original: Persian
Solving fourth-order boundary value problem with orthogonal wavelet basis

Mohammadreza Foroutan * Pages 153-175

In the presented paper, an effective method based upon Legendre wavelet function is proposed for ‎the solution of the singular fourth-order boundary value problem with mixed boundary conditions. ‎The properties of Legendre wavelet function are first presented and then we introduce the ‎construction method of wavelet basis in W_2^5 [0,1] by orthogonal wavelet basis in W_2^1 [0,1]. The ‎ε-approximate solution was defined and then it was proved to be the optimal solution. In addition, the ‎stability and convergence for the method in W_2^5 [0,1] space are discussed. Numerical illustrations ‎are investigated to show the reliability and efficiency of the proposed method.‎

Keywords: Legendre polynomials, Legendre wavelet basis, ε-approximate ‎ splution, Stability analysis, convergence order

Abstract View Paper Research/Original Article Original: Persian
The Holder-McCarthy vector state inequality and some of its consequences

Mohsen Kian * Pages 177-192

In this paper, we study the Holder McCarthy vector state inequality and give improvements for some well-known inequalities in vector state versions. In particular, we give a precise estimate of the triangle inequality for p-norms on vectors as \begin{align*} \left(\frac{\|\mathbf{\mathrm{u}}+\mathbf{\mathrm{v}}\|_p}{\|\mathbf{\mathrm{u}}\|_p+\|\mathbf{\mathrm{v}}\|_p}\right)^p\begin{cases}\leq 1 - \alpha (p) \left\|\mathbf{\mathrm{w}}\right\|_p^p& \,\, p\geq 2;\\\geq 1 - \alpha (p) \left\|\mathbf{\mathrm{w}}\right\|_p^p & \,\, 1\leq p\leq 2;\\= 1 - \alpha (2) \left\|\mathbf{\mathrm{w}}\right\|_2^2 &\,\, p=2,\end{cases}\qquad \qquad( \mathbf{\mathrm{u}},\mathbf{\mathrm{v}}\in \mathbb{R}^n)\end{align*}

Keywords: vector state inequality, positive matrix, superquadratic function

Abstract View Paper Research/Original Article Original: Persian
Construction of uniform excesses frames using tensor product

Ahmad Ahmadi *, Somayeh Afshar Jahnshahi Pages 193-211

.Various types of frames have been introduced to solve the problems that arise in the application of frames in different fields of science. Due to problems such as missing or changing frame coefficients that occurred during signal transmission, frames with uniform excess emerged. The tensor product is the basic ingredient in signal processing, to extend one-dimensional methods of filtering and compression of sound to higher dimensions and to use them in image processing. ‎‎In this paper, a method for constructing frames with uniform excess by tensor product of frames will be presented, and with the help of a quantitative criterion of redundancy, this method is compared with other methods of making frames with uniform excess that are expressed on the basis of the union of frames.

Keywords: Frame, Tensor product, uniform excess frame, Hilbert space

Abstract View Paper Research/Original Article Original: Persian

علمی مصوب

مجله موجکها و جبر خطی

Wavelets and Linear Algebra

دوفصلنامه علوم پایه به زبان فارسی و انگلیسی

آخرین شماره | آرشیو

ISSN: 2383-1936 eISSN: 2476-3926

صاحب امتیاز:

دانشگاه ولی عصر رفسنجان

مدیر مسئول:

دکتر علی آرمندنژاد

سردبیر:

دکتر محمدعلی دهقان

تلفن نشریه: ۰۳۴-۳۱۳۱۲۲۶۰

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فهرست مطالب

مجله موجکها و جبر خطی سال نهم شماره 2 (Autumn and Winter 2022)

مجله موجکها و جبر خطی

Wavelets and Linear Algebra

مجله موجکها و جبر خطی
سال نهم شماره 2 (Autumn and Winter 2022)