Disjoint topological transitivity for cosine operator functions on groups

In this paper, we study finite sequences of operators, generated by the powers of weighted translations on discrete groups, and give sufficient conditions for such sequences to be disjoint topologically transitive and mixing in terms of the group elements and weights. The sequences of operators are cosine operator functions. Moreover, we also obtain necessary conditions for cosine operator functions to be disjoint transitive and mixing.

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Topological transitivity for cosine operator functions on groups

Topology and its Applications ◽

10.1016/j.topol.2015.05.005 ◽

2015 ◽

Vol 191 ◽

pp. 48-57 ◽

Cited By ~ 3

Author(s):

Chung-Chuan Chen

Keyword(s):

Topological Transitivity ◽

Cosine Operator ◽

Operator Functions ◽

Cosine Operator Functions

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Approximation theorems for cosine operator functions

Acta Mathematica Academiae Scientiarum Hungaricae ◽

10.1007/bf01896469 ◽

1977 ◽

Vol 29 (1-2) ◽

pp. 69-76 ◽

Cited By ~ 8

Author(s):

B. Nagy

Keyword(s):

Approximation Theorems ◽

Cosine Operator ◽

Operator Functions ◽

Cosine Operator Functions

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Growth order and stability of semigroups and cosine operator functions

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2009.01.049 ◽

2009 ◽

Vol 357 (2) ◽

pp. 340-348 ◽

Cited By ~ 3

Author(s):

Sen-Yen Shaw

Keyword(s):

Growth Order ◽

Cosine Operator ◽

Operator Functions ◽

Cosine Operator Functions

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Semigroups of operators, cosine operator functions, and linear differential equations

Journal of Soviet Mathematics ◽

10.1007/bf01138948 ◽

1991 ◽

Vol 54 (4) ◽

pp. 1042-1129 ◽

Cited By ~ 11

Author(s):

V. V. Vasil'ev ◽

S. G. Krein ◽

S. I. Piskarev

Keyword(s):

Differential Equations ◽

Linear Differential Equations ◽

Semigroups Of Operators ◽

Cosine Operator ◽

Operator Functions ◽

Cosine Operator Functions ◽

Linear Differential

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Cosine operator functions and the abstract Cauchy problem

Periodica Mathematica Hungarica ◽

10.1007/bf02017937 ◽

1976 ◽

Vol 7 (3-4) ◽

pp. 213-217 ◽

Cited By ~ 13

Author(s):

B. Nagy

Keyword(s):

Cauchy Problem ◽

Abstract Cauchy Problem ◽

Cosine Operator ◽

Operator Functions ◽

Cosine Operator Functions

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Operator Matrices as Generators of Cosine Operator Functions

Integral Equations and Operator Theory ◽

10.1007/s00020-004-1357-x ◽

2005 ◽

Vol 54 (3) ◽

pp. 441-464 ◽

Cited By ~ 9

Author(s):

Delio Mugnolo

Keyword(s):

Operator Matrices ◽

Cosine Operator ◽

Operator Functions ◽

Cosine Operator Functions

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Chaos for Cosine Operator Functions on Groups

Abstract and Applied Analysis ◽

10.1155/2014/603234 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Chung-Chuan Chen

Keyword(s):

Locally Compact Group ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Locally Compact ◽

Direct Sum ◽

Cosine Operator ◽

Weight Condition ◽

Operator Functions ◽

Cosine Operator Functions ◽

Necessary And Sufficient

Let1≤p<∞andGbe a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue spaceLp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously. We also give a necessary and sufficient condition for the direct sum of a sequence of cosine operator functions to be chaotic.

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