scholarly journals Operator Matrices as Generators of Cosine Operator Functions

2005 ◽  
Vol 54 (3) ◽  
pp. 441-464 ◽  
Author(s):  
Delio Mugnolo
Keyword(s):  
Operator Matrices ◽  
Cosine Operator ◽  
Operator Functions ◽  
Cosine Operator Functions

scholarly journals Chaos for Cosine Operator Functions on Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
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.

scholarly journals Disjoint topological transitivity for cosine operator functions on groups

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2413-2423
Author(s):  
Chung-Chuan Chen
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Discrete Groups ◽  
Topological Transitivity ◽  
Topologically Transitive ◽  
Cosine Operator ◽  
Finite Sequences ◽  
Operator Functions ◽  
Cosine Operator Functions

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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