Czechoslovak Mathematical Journal, first online, pp. 1-26


Polynomial expansiveness and admissibility of weighted Lebesgue spaces

Pham Viet Hai

Received April 29, 2019.   Published online August 18, 2020.

Abstract:  The paper investigates the interaction between the notions of expansiveness and admissibility. We consider a polynomially bounded discrete evolution family and define an admissibility notion via the solvability of an associated difference equation. Using the admissibility of weighted Lebesgue spaces of sequences, we give a characterization of discrete evolution families which are polynomially expansive and also those which are expansive in the ordinary sense. Thereafter, we apply the main results in order to infer continuous-time characterizations for the notions of expansiveness through the solvability of an associated integral equation.
Keywords:  polynomial expansiveness; evolution family
Classification MSC:  34E05, 34D05
DOI:  10.21136/CMJ.2020.0195-19

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Affiliations:   Pham Viet Hai, Faculty of Mathematics, Mechanics and Informatics, University of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam; and Thang Long Institute of Mathematics and Applied Sciences, Thang Long University, Nghiem Xuan Yem Road, Hoang Mai District, Vietnam, e-mail: phamviethai86@gmail.com


 
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