The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new paradigm vector-valued setting, which motivated by complex conjugate vectors range space real matrix and Paley-Wiener space, also determination vector field defined on graph relative between neighboring vertices. prov...

In this paper, we consider a broad class of interpolation problems, for both scalarand vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation ...

This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given kernel as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occu...

The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space de…ned by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including ...

We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional

We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional

We consider the sigma-finite measures in the space of vector-valued distributions on the manifold X with characteristic functional