Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2018
Volume
Vol. 38
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 38 (2018)
Projects
Pages
Articles
Adelic analysis and functional analysis on the finite Adele ring
(Wydawnictwa AGH, 2018) Cho, Ilwoo
In this paper, we study operator theory on the $∗$-algebra $\mathcal{M}_{\mathcal{P}}$, consisting of all measurable functions on the finite Adele ring $A_{\mathbb{Q}}$, in extended free-probabilistic sense. Even though our $∗$-algebra $\mathcal{M}_{\mathcal{P}}$ is commutative, our Adelic-analytic data and properties on $\mathcal{M}_{\mathcal{P}}$ are understood as certain free-probabilistic results under enlarged sense of (noncommutative) free probability theory (well-covering commutative cases). From our free-probabilistic model on $A_{\mathbb{Q}}$, we construct the suitable Hilbert-space representation, and study a $C∗$-algebra $M_{\mathcal{P}}$ generated by $\mathcal{M}_{\mathcal{P}}$ under representation. In particular, we focus on operator-theoretic properties of certain generating operators on $M_{\mathcal{P}}$.
Existence results for Kirchhoff type systems with singular nonlinearity
(Wydawnictwa AGH, 2018) Firouzjai A.; Afrouzi, Ghasem Alizadeh; Talebi, Sorayya
Using the method of sub-super solutions, we study the existence of positive solutions for a class of singular nonlinear semipositone systems involving nonlocal operator.
Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
(Wydawnictwa AGH, 2018) Katō, Mitsuo; Mano, Toshiyuki; Sekiguchi, Jirō
A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.
Trace formulas for perturbations of operators with Hilbert-Schmidt resolvents
(Wydawnictwa AGH, 2018) Sedai, Bishnu Prasad
Trace formulas for self-adjoint perturbations $V$ of self-adjoint operators H such that $V$ is in Schatten class were obtained in the works of L.S. Koplienko, M.G. Krein, and the joint paper of D. Potapov, A. Skripka and F. Sukochev. In this article, we obtain an analogous trace formula under the assumptions that the perturbation $V$ is bounded and the resolvent of $H$ belongs to Hilbert-Schmidt class.
Stochastic differential equations for random matrices processes in the nonlinear framework
(Wydawnictwa AGH, 2018) Stihi, Sara; Boutabia, Hacène; Meradji, Selma
In this paper, we investigate the processes of eigenvalues and eigenvectors of a symmetric matrix valued process $X_{t}$, where $X_{t}$ is the solution of a general SDE driven by a $G$-Brownian motion matrix. Stochastic differential equations of these processes are given. This extends results obtained by P. Graczyk and J. Malecki in [Multidimensional Yamada-Watanabe theorem and its applications to particle systems, J. Math. Phys. 54 (2013), 021503].