scholarly journals On the Fekete–Szegö type functionals for functions which are convex in the direction of the imaginary axis

2021 ◽  
Vol 358 (11-12) ◽  
pp. 1213-1226
Author(s):  
Paweł Zaprawa
Keyword(s):  
Imaginary Axis

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

An Algorithm for Factoring Hermitian Matrix Polynomials Relative to the Imaginary Axis

1996 ◽  
Vol 29 (1) ◽  
pp. 1263-1268
Author(s):  
Chyi Hwang ◽  
Bo-Win Lin ◽  
Tong-Yi Guo
Keyword(s):  
Imaginary Axis ◽  
Hermitian Matrix ◽  
Matrix Polynomials

scholarly journals Computation of Green’s Function of the Bounded Solutions Problem

2018 ◽  
Vol 18 (4) ◽  
pp. 673-685 ◽  
Author(s):  
Vitalii G. Kurbatov ◽  
Irina V. Kurbatova
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Numerical Experiments ◽  
Imaginary Axis ◽  
Approximate Calculation ◽  
Special Function ◽  
Bounded Solution ◽  
Free Term ◽  
Bounded Solutions ◽  
Square Matrix

AbstractIt is well known that the equation {x^{\prime}(t)=Ax(t)+f(t)}, where A is a square matrix, has a unique bounded solution x for any bounded continuous free term f, provided the coefficient A has no eigenvalues on the imaginary axis. This solution can be represented in the formx(t)=\int_{-\infty}^{\infty}\mathcal{G}(t-s)f(s)\,ds.The kernel {\mathcal{G}} is called Green’s function. In this paper, for approximate calculation of {\mathcal{G}}, the Newton interpolating polynomial of a special function {g_{t}} is used. An estimate of the sensitivity of the problem is given. The results of numerical experiments are presented.

Note on roots location of a symmetric polynomial with respect to the imaginary axis

2012 ◽  
Vol 60 (4) ◽  
pp. 499-510
Author(s):  
Hui-Feng Hao ◽  
Yong-Jian Hu ◽  
Gong-Ning Chen
Keyword(s):  
Imaginary Axis ◽  
Symmetric Polynomial

scholarly journals Spectrum of the M5-traveling waves

2020 ◽  
Vol 15 ◽  
pp. 66
Author(s):  
Salvador Cruz-García
Keyword(s):  
Essential Spectrum ◽  
Traveling Waves ◽  
Imaginary Axis ◽  
Weighted Space ◽  
Cell Movement ◽  
Mesenchymal Cell ◽  
Weight Functions ◽  
Dimensional Version ◽  
The One ◽  
Linearized Operator

In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M5-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in L2(ℝ; ℂ3) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space Lw2(ℝ; ℂ3) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space Lwα2(ℝ; ℂ2) × Lwε2(ℝ; ℂ) the essential spectrum lies on {Reλ<0}, outside the imaginary axis.

Sign in / Sign up

Export Citation Format

Share Document