If z is a function from the real line R′ to a real Hilbert space X then the covariance function ϱ of z is defined by ϱ(t, s) ≡ (z(t), z(s)). It is proved that the function (z(·), y) is of bounded ...

Hilbert spaces provide a fundamental mathematical framework for analysing infinite-dimensional vector spaces endowed with an inner product. In the context of stochastic processes, these spaces serve ...

Hilbert space theory and operator algebras provide a robust framework for analysing linear operators and their spectral properties, which are pivotal in both pure and applied mathematics. Hilbert ...