Polynomial expansiveness and admissibility of weighted Lebesgue spaces

Hai, Pham Viet

Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 111-136

Abstract (VO)

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.

Détail

DOI : 10.21136/CMJ.2020.0195-19

Classification : 34D05, 34E05
Keywords: polynomial expansiveness; evolution family

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