DISTRIBUTIONALLY CHAOTIC FAMILIES OF OPERATORS ON FRECHET SPACES

被引：15

作者：

Alberto Conejero, J. ^{[1
]}

Kostic, Marko ^{[2
]}

Miana, Pedro J. ^{[3
,4
]}

Murillo-Arcila, Marina ^{[1
]}

机构：

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia, Spain

[2] Univ Novi Sad, Fac Tech Sci, Novi Sad, Serbia

[3] Univ Zaragoza, Dept Matemat, Zaragoza, Spain

[4] Univ Zaragoza, IUMA, Zaragoza, Spain

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 05期

关键词：

Distributional chaos; integrated semigroups; C-regularized semigroups; cosine functions; abstract time-fractional equations; hypercyclicity; well-posedness; Frechet spaces; STRONGLY CONTINUOUS SEMIGROUPS; HYPERCYCLICITY; C-0-SEMIGROUPS; DYNAMICS; BEHAVIOR;

D O I：

10.3934/cpaa.2016022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.

引用

页码：1915 / 1939

页数：25

共 57 条

[31]

Dembart B., 1974, Journal of Functional Analysis, V16, P123, DOI 10.1016/0022-1236(74)90061-5

[32] Hypercyclic and chaotic semigroups of linear operators [J].

Desch, W ;

Schappacher, W ;

Webb, GF .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1997, 17 :793-819

[33] A linear chaotic quantum harmonic oscillator [J].

Duan, J ;

Fu, XC ;

Liu, PD ;

Manning, A .

APPLIED MATHEMATICS LETTERS, 1999, 12 (01) :15-19

[34] The imaginary point spectrum and hypercyclicity [J].

EL Mourchid, Samir .

SEMIGROUP FORUM, 2006, 73 (02) :313-316

[35] CHAOTIC SOLUTION FOR THE BLACK-SCHOLES EQUATION [J].

Emamirad, Hassan ;

Goldstein, Gisele Ruiz ;

Goldstein, Jerome A. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (06) :2043-2052

[36] Strongly continuous semigroups on some Frechet spaces [J].

Frerick, Leonhard ;

Jorda, Enrique ;

Kalmes, Thomas ;

Wengenroth, Jochen .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 412 (01) :121-124

[37] OPERATORS WITH DENSE, INVARIANT, CYCLIC VECTOR MANIFOLDS [J].

GODEFROY, G ;

SHAPIRO, JH .

JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 98 (02) :229-269

[38] SOME REMARKS ON INFINITESIMAL GENERATORS OF ANALYTIC SEMIGROUPS [J].

GOLDSTEIN, JA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 22 (01) :91-+

[39] Hypercyclicity for the Elements of the Commutant of an Operator [J].

Gonzalez, Manuel ;

Leon-Saavedra, Fernando .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2014, 80 (02) :265-274

[40]

Grosse-Erdmann K.-G., 2011, Linear Chaos

← 1 2 3 4 5 6 →