, 2023 Let $T$ be an operator on Banach space $X$ that is similar to $- T$ via an involution $U$. Then $U$ decomposes the Banach space $X$ as $X = X_1 \oplus X_2$ with respect to which decomposition we have $U = \left(\begin{matrix} I_1 & 0 \\ 0 & -I_2 \end ...
Drnovšek, Roman
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Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations over Generalized Reflexive Matrices [PDF]
, 2016 The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete ...
Masoud Hajarian
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A variant of d’Alembert’s matrix functional equation [PDF]
, 2020 The aim of this paper is to characterize the solutions Φ:G→M2(ℂ) of the following matrix functional equations\frac{Φ(xy)+Φ(σ(y)x)}{2} = Φ(x)Φ(y), x,y∈G,and\frac{Φ(xy)-Φ(σ(y)x)}{2} = Φ(x)Φ(y), x,y∈G,where G is a group that need not be abelian, and σ:G→G ...
Aissi, Youssef +2 more
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On the equivalence of pre-Schroder equations [PDF]
, 2007 In the paper the equivalence of the system of two pre-Schr¨oder functional equations (equations (Sn), (Sm) for m > n 3, n,m 2 N) and the whole system (S), is considered. The results solve the problem of Gy.
Kalinowski, Józef
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Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation, I. the least squares solution. [PDF]
, 2011 In this paper a state space formula is derived for the least squares solution X of the corona type Bezout equation G(z)X(z) =
A. C. M. Ran +27 more
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The Extended Leibniz Rule and Related Equations in the Space of Rapidly Decreasing Functions [PDF]
, 2018 We solve the extended Leibniz rule T(f•g)=Tf•Ag+Af•Tg for operators T and A in the space of rapidly decreasing functions in both cases of complex and real-valued functions.Ми розв язуємо узагальнене правило Лейбниця T(f•g)=Tf•Ag+Af•Tg для операторiв T ...
König, Hermann, Milman, Vitali
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On representation by exit laws for some Bochner subordinated semigroups [PDF]
, 2008 This paper is devoted to the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of kernels acting on L2(m).
Hmissi, Mohamed, Mejri, Hassen
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Positive solutions for a nonlinear parameter-depending algebraic system [PDF]
, 2015 Through variational methods, the existence of positive solutions for a nonlinear parameter-depending algebraic system is investigated. The main tools used are some very recent critical points theorems on finite dimensional Banach spaces and a new ...
Bonanno G., Candito P., D'Agui G.
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Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle [PDF]
, 2010 In this paperwe characterize sequences of orthogonal polynomials on the unit circle whose Carathéodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of matrix Sylvester differential equations.
Branquinho, A., Rebocho, M. N.
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The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem [PDF]
, 2005 In this paper, the structure of several convex cones that arise in the study of Lyapunov functions is investigated. In particular, the cones associated with quadratic Lyapunov functions for both linear and non-linear systems are considered, as well as ...
Mason, Oliver, Shorten, Robert N.
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