Mathematics - Research News

Symmetric Lyapunov center theorem for orbit with nontrivial isotropy group

 Mathematics - Research News
 06 February 2020
Marta Kowalczyk, Ernesto Pérez-Chavela, Sławomir Rybicki. Source: Advances in Differential Equations, Volume 25, Number 1/2, 1--30.Abstract: In this article, we prove two versions of the Lyapunov center theorem for symmetric potentials. We consider a second order autonomous system $$ \ddot...

Noncompactness of Fourier convolution operators on Banach function spaces

 Mathematics - Research News
 31 October 2019
Cláudio A. Fernandes, Alexei Y. Karlovich, Yuri I. Karlovich. Source: Annals of Functional Analysis, Volume 10, Number 4, 553--561.Abstract: Let $X(\mathbb{R})$ be a separable Banach function space such that the Hardy–Littlewood maximal operator $M$ is bounded on $X(\mathbb{R})$ and on its...

Generalized frames for controlled operators in Hilbert spaces

 Mathematics - Research News
 31 October 2019
Dongwei Li, Jinsong Leng. Source: Annals of Functional Analysis, Volume 10, Number 4, 537--552.Abstract: Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled...

Approximate duals and morphisms of Hilbert $C^{\ast}$ -modules

 Mathematics - Research News
 31 October 2019
Morteza Mirzaee Azandaryani. Source: Annals of Functional Analysis, Volume 10, Number 4, 525--536.Abstract: In the following we show that, under some conditions, $\varphi$ -morphisms preserve duals and approximate duals of frames in Hilbert $C^{\ast }$ -modules. Moreover, using $\varphi $...

Wigner’s theorem on the Tsirelson space $T$

 Mathematics - Research News
 31 October 2019
Yuanxia Li, Dongni Tan. Source: Annals of Functional Analysis, Volume 10, Number 4, 515--524.Abstract: We say that a map $f:X\rightarrow Y$ between two real normed spaces is a phase-isometry if $\{\|f(x)+f(y)\|,\|f(x)-f(y)\|\}=\{\|x+y\|,\|x-y\|\}$ holds for all $x,y\in X$ . Two maps...

Ky Fan minimax inequalities for set-valued mappings on dense sets

 Mathematics - Research News
 31 October 2019
Chuang-Liang Zhang. Source: Annals of Functional Analysis, Volume 10, Number 4, 496--508.Abstract: We give a natural Ky Fan minimax inequality version of set-valued maps, and we deal with a type of vector equilibrium problem for set-valued mappings on a special dense set not on the whole domain....

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