On linear equations in Hilbert space

Real-linear Operators on Quaternionic Hilbert Space

The main result is that any continuous real-linear operator A on a quaternionic Hubert space has a unique decomposition A=A0+iiAl + izAi+iiA3, where the A„ are continuous linear operators and (fi,f2,'3) is any right-handed orthonormal triad of vector quaternions. Other results concern the place of the colinear and complex-linear operators in this characterisation and the effect on the Av of a r...

Nonlinear Functional Integrodifferential Equations in Hilbert Space

Let X be a Hilbert space and let Ω ⊂ Rn be a bounded domain with smooth boundary ∂Ω. We establish the existence and norm estimation of solutions for the parabolic partial functional integro-differential equation in X by using the fundamental solution.

On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space

On stochastic fractional Volterra equations in Hilbert space

In this paper, stochastic Volterra equations, particularly fractional, in Hilbert space are studied. Sufficient conditions for mild solutions to be strong solutions are provided. Several examples of Volterra equations having strong solutions are given, as well.

Cointegrated linear processes in Hilbert space

Consider a sequence X = (X0,X1, . . .) of random elements of a real separable Hilbert space H , whose €rst di‚erence is a standard linear process with long run covariance operator Λ. We show that, under a mild summability condition, the set of vectors x ∈ H for which 〈Xt ,x〉 is stationary given a suitable initialization X0 is the kernel of Λ. We call this space the cointegrating space, and its ...