RT journal article
T1 Maximal ℓp-regularity for discrete time volterra equations with delay
A1 Lizama, Carlos
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 volterra equations
K1 maximal $ell_p$-regularity
K1 R-bounded, discrete wave equation
K1 discrete kuznetsov equation
AB In this paper we investigate the existence and uniqueness of solutions  belonging to the vector-valued space  $ \ell_p(\Z,X)$ by using Blunck's theorem on the equivalence between operator-valued $\ell_p$-multipliers and the notion of $R$-boundedness for the discrete time volterra equation with delay given by$$	u(n) =  \sum_{j=-\infty}^{n}b(n-j)Au(j)+\sum_{j=1}^k \beta_j u(n-\tau_j) + f(n), \qquad n \in \mathbb{Z},$$where $A$ is a closed linear operator with domain $D(A)$ defined on a Banach space $X$ and $b\in\ell_1(\Z)$ verifies suitable conditions such as $1$-regularity. We characterize maximal  $\ell_p$-regularity of solutions of such problems in terms of the data and an spectral condition and we provide optimal estimates. Moreover, we illustrate our results providing  different models that label into our general scheme such as the discrete time wave and Kuznetsov equations.
PB Taylor & Francis
SN 1563-5120
YR 2019
FD 2019
LK http://hdl.handle.net/10498/35373
UL http://hdl.handle.net/10498/35373
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026