arXiv subjects

Jose A. Franco

Publications and source records attributed to Jose A. Franco.

3 recordsLinked to original sources

arXiv2019

Some Geometric Properties of Matrix Means with respect to Different Distance Function

In this paper we study the monotonicity, in-betweenness and in-sphere properties of matrix means with respect to Bures-Wasserstein, Hellinger and Log-Determinant metrics. More precisely, we show that the matrix power means (Kubo-Ando and non-Kubo-Ando extensions) satisfy the in-betweenness property in the Hellinger metric. We also show that for two positive definite matrices $A$ and $B$, the curve of weighted Heron means, the geodesic curve of the arithmetic and the geometric mean lie inside the sphere centered at the geometric mean with the radius equal to half of the Log-Determinant distance between $A$ and $B$.

math.FA↗

arXiv2014

Global Actions of the Lie Symmetries of the Nonlinear Filtration Equation

The classification of the Lie point symmetries of the nonlinear filtration equation gives the generic case and three special cases. By restricting to a special class of functions, we show that the Lie symmetries of the nonlinear filtration equation exponentiate to a global action of a solvable Lie group in the generic case and two of the three special cases. We show that the action of the Lie point symmetries cannot be globalized for the third special case.

math.RT↗

arXiv2013

On the n-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group

By restricting to a special class of smooth functions, the local action of the symmetry group is globalized. This special class of functions is constructed using parabolic induction.

math.RT↗