Quaternionic Hilbert spaces play an important role in applied physical sciences especially quantum physics. In this paper, the operator valued frames on quaternionic are introduced and studied. terms of a class partial isometries spaces, parametrization Parseval is obtained. We extend to many properties vector process. Moreover, we show that all can be obtained from single frame. Finally, sever...

* Correspondence: [email protected] Department of Mathematics Faculty Of Science, Naresuan University Phitsanulok 65000, Thailand Full list of author information is available at the end of the article Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To o...

In this paper we prove the existence of solutions to the following third order differential inclusion:  x(3)(t) ∈ F (t, x(t), ẋ(t), ẍ(t)) + G(x(t), ẋ(t), ẍ(t)), a.e. on [0, T ] x(0) = x0, ẋ(0) = u0, ẍ(0) = v0, and ẍ(t) ∈ S,∀t ∈ [0, T ], where F : [0, T ]×H×H×H → H is a continuous set-valued mapping, G : H× H × H → H is an upper semi-continuous set-valued mapping with G(x, y, z) ⊂ ∂g(z) where g...

A mono-component is a real-valued signal of finite energy that has non-negative instantaneous frequencies, which may be defined as the derivative of the phase function of the given real-valued signal through the approach of canonical amplitude-phase modulation. We study in this article how the amplitude is determined by its phase in a canonical amplitude-phase modulation. Our finding is that su...

An extensive literature in economics uses a continuum of random variables to model individual random shocks imposed on a large population. Let H denote the Hilbert space of square-integrable random variables. A key concern is to characterize the family of all H-valued functions that satisfy the law of large numbers when a large sample of agents is drawn at random. We use the iterative extension...

We propose a method to learn simultaneously a vector-valued function and a kernel between its components. The obtained kernel can be used both to improve learning performance and to reveal structures in the output space which may be important in their own right. Our method is based on the solution of a suitable regularization problem over a reproducing kernel Hilbert space of vector-valued func...

This paper presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) formulation for the problem of learning an unknown functional dependency between a structured input space and a structured output space, in the Semi-Supervised Learning setting. Our formulation includes as special cases Vector-valued Manifold Regularization and Multi-view Learning, thus provides in particular a...