We show the remarkable fact that the nonlocal property of the discrete N-dimensional
fractional Laplacian acting in the second variable of the lattice N× ZN can be exchanged …

This note is concerned with two families of operators related to the fractional Laplacian, the
first arising from the Caffarelli-Silvestre extension problem and the second from the fractional …

In this paper we consider the heat semigroup $\{W_t\} _ {t> 0} $ defined by the combinatorial
Laplacian and two subordinated families of $\{W_t\} _ {t> 0} $ on homogeneous trees $ X …

This work deals with the extension problem for the fractional Laplacian on Riemannian
symmetric spaces G/K of noncompact type and of general rank, which gives rise to a family …

We study the asymptotic behavior of solutions to the multidimensional diffusion (heat)
equation with continuous time and discrete space. We focus on initial-value problems with …

In this paper, we characterize the discrete Hölder spaces by means of the heat and Poisson
semigroups associated with the discrete Laplacian. These characterizations allow us to get …

In this paper we completely solve the open problem of finding the fundamental solution of
the semidiscrete fractional-spatial damped wave equation. We combine operator theory and …

In this paper we prove characterizations of the discrete Besov spaces in terms of the heat
and Poisson semigroups associated with the discrete Laplacian that will allow us to prove …

In this paper we analyze some classical operators in harmonic analysis associated to the
multidimensional discrete Laplacian\[\Delta_N f (\mathbf {n})=\sum_ {i= 1}^{N}(f (\mathbf …

In this article, we study the asymptotic behavior and decay of the solution of the fully discrete
heat problem. We show basic properties of its solutions, such as the mass conservation …