The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an introduction to matrix-valued kernels and their relevant differential properties, we explore exte...

Recent research has focused on feed-forward networks with complex weights and activation values such as GK92, Hir92b, Hir92a, Hir93]. This paper extends this formalism to feed-forward networks with weight and activation values taken from a Cliiord algebra (see also PB92, PB94b]). A Cliiord algebra is a multi-dimensional generalization of the complex numbers and the Quaternions. Essentially a Cl...

The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

The aim of this paper is to introduce the notion Perov–Ćirić–Prešić-type Θ-contractions and obtain some generalized fixed point theorems in setting vector-valued metric spaces. We derive results as consequences our main results. A nontrivial example also provided support validity established As an application, we investigate solution a semilinear operator system Banach space.