Czechoslovak Mathematical Journal, Vol. 71, No. 1, pp. 111-136, 2021
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
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: email@example.com