Suppose I have a vector-valued function f(x) = y, where x and y are both vectors of some length (same or different length). f could be evaluated over a regular grid of x values, producing a set of y ...

Abstract: This paper presents a preliminary implementation of a general modeling framework for vector-valued functions based on a multi-output kernel Ridge regression (KRR). The proposed approach is ...

Abstract: This paper presents a kernel-based nonlinear mixing model for hyperspectral data, where the nonlinear function belongs to a Hilbert space of vector valued functions. The proposed model ...

The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function ; that is, for ...

In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and ...