arXiv subjects

Luis Acuna Valverde

Publications and source records attributed to Luis Acuna Valverde.

6 recordsLinked to original sources

arXiv2019

On the heat content for the poisson kernels over the unit ball in the euclidean space

This paper studies, by employing analytical tools, the small time behavior of the heat content for the Poisson kernel over the unit ball in $\Rd$, $d\geq 2$ by working with its related set covariance function. As a result, we obtain a representation for the third term in the expansion of the heat content over the unit ball and provide the explicit form of the this term in the particular cases $d=2$ and $d=3$.

math.PR↗

arXiv2016

On the one--dimensional spectral Heat content for stable processes

This paper provides the second term in the small time asymptotic expansion of the spectral heat content of a rotationally invariant $α$--stable process, $0<α\leq 2$, for the interval $(a,b)$. The small time behavior of the spectral heat content turns out to be linked to the distribution of the supremum and infimum processes.

math.PR↗

arXiv2016

Heat content estimates over sets of finite perimeter

This paper studies by means of standard analytic tools the small time behavior of the heat content over a bounded Lebesgue measurable set of finite perimeter by working with the set covariance function and by imposing conditions on the heat kernels. Applications concerning the heat kernels of rotational invariant $α$-stable processes are given.

math.PR↗

arXiv2015

Heat content for stable processes in domains of $\R^d$

This paper studies the small time behavior of the heat content of rotationally invariant $α$--stable processes, $0<α\leq 2$, in domains in $\R^d$. Unlike the asymptotics for the heat trace, the behavior of the heat content differs depending on the ranges $0<α<1$, $α=1$ and $1<α\leq 2$.

math.PR↗

arXiv2014

A decomposition for additive functional of Levy processes

Motivated by the recent results of Nualart and Xu \cite{Nualart} concerning limits laws for occupation times of one dimensional symmetric stable processes, this paper proves a decomposition for functionals of one dimensional symmetric Lévy processes under certain conditions on the characteristic exponent and computes the moments of the decomposition.

math.PR↗

arXiv2012

Trace Asymptotics for Fractional Schrodinger Operators

This paper proves an analogue of a result of Banuelos and Sa Barreto on the asymptotic expansion for the trace of Schrodinger operators on $\R^d$ when the Laplacian $Δ$, which is the generator of the Brownian motion, is replaced by the non-local integral operator $Δ^{α/2}$, $0<α<2$, which is the generator of the symmetric stable process of order $α$. These results also extend recent results of Banuelos and Yildirim where the first two coefficients for $Δ^{α/2}$ are computed. Some extensions to Schrodinger operators arising from relativistic stable and mixed stable processes are obtained.

math.PR↗