in this article we consider the sequences of sample and population covariance operators for a sequence of arrays of hilbertian random elements. then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

The statistical analysis of covariance operators in a functional data analysis setting is considered. Many suitable distances to compare covariance operators are presented and in particular the problem of estimating the average covariance operators among different groups is addressed. Finally, an applied problem in which this methodology has proved useful is introduced, namely, exploring phonet...

Let HI (resp., HZ) be a real and separable Hilbert space with Borel a-field f 1 (resp., f 2), and let (HIXH Z ' f 1 x f 2) be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on (HIXH Z ' f 1 x f 2), i.e., joint measures, and the projections of such measures on (HI' f 1) and (HZ' f 2). In particular, the class of all...

Among all classes of pseudo-differential operators only the Weyl operators enjoy the property of symplectic covariance with respect to conjugation by elements of the metaplectic group. In this paper we show that there is, however, a weaker form of symplectic covariance for Shubin’s τ -dependent operators, in which the intertwiners no longer are metaplectic, but still are invertible non-unitary ...