Polynomial expansiveness and admissibility of weighted Lebesgue spaces

Pham Viet Hai

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 111-136
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Hai, Pham Viet. "Polynomial expansiveness and admissibility of weighted Lebesgue spaces." Czechoslovak Mathematical Journal (2021): 111-136. <http://eudml.org/doc/297054>.

@article{Hai2021,
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.},
author = {Hai, Pham Viet},
journal = {Czechoslovak Mathematical Journal},
keywords = {polynomial expansiveness; evolution family},
language = {eng},
number = {1},
pages = {111-136},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Polynomial expansiveness and admissibility of weighted Lebesgue spaces},
url = {http://eudml.org/doc/297054},
year = {2021},
}

TY - JOUR
AU - Hai, Pham Viet
TI - Polynomial expansiveness and admissibility of weighted Lebesgue spaces
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 111
EP - 136
AB - 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.
LA - eng
KW - polynomial expansiveness; evolution family
UR - http://eudml.org/doc/297054
ER -

References

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