arXiv subjects

Mario H. Castro

Publications and source records attributed to Mario H. Castro.

3 recordsLinked to original sources

arXiv2019

Eigenvalue decay of positive integral operators on compact two-point homogeneous spaces

We generalize and extend results on decay rates of singular values or eigenvalues of positive integral operators from unit spheres to two-point homogeneous spaces. The rates we present depend upon the order of the Laplace-Beltrami operator used to define the smoothness conditions on generating kernels, the Schatten class containing the integral operator generated by the derivative of the generating kernel and the dimension of the space.

math.FA↗

arXiv2018

Characterization of Strict Positive Definiteness on products of complex spheres

In this paper we consider Positive Definite functions on products $Ω_{2q}\timesΩ_{2p}$ of complex spheres, and we obtain a condition, in terms of the coefficients in their disc polynomial expansions, which is necessary and sufficient for the function to be Strictly Positive Definite. The result includes also the more delicate cases in which $p$ and/or $q$ can be $1$ or $\infty$. The condition we obtain states that a suitable set in $\mathbb{Z}^2$, containing the indexes of the strictly positive coefficients in the expansion, must intersect every product of arithmetic progressions.

math.CA↗

arXiv2012

Traceability of positive integral operators in the absence of a metric

We investigate the traceability of positive integral operators on $L^2(X,μ)$ when $X$ is a Hausdorff locally compact second countable space and $μ$ is a non-degenerate, $σ$-finite and locally finite Borel measure. This setting includes other cases proved in the literature, for instance the one in which $X$ is a compact metric space and $μ$ is a special finite measure. The results apply to spheres, tori and other relevant subsets of the usual space $\mathbb{R}^m$.

math.FA↗