Rochberg’s coboundary theorem provides conditions under which the equation $$(I-T)y = x$$ is solvable in y. Here T a unilateral shift on Hilbert space, I identity operator and x given vector. The are expressed terms of Wold-type decomposition determined by growth iterates at x. We revisit prove following result. Let be an isometry acting space $$\mathcal H$$ let $$x \in \mathcal . Suppose that ...

We introduce Markovian cocycle perturbations of the groups of transformations associated with the classical and quantum stochastic processes with stationary increments, which are characterized by a localization of the perturbation to the algebra of events of the past. It is namely the definition one needs because the Markovian perturbations of the Kolmogorov flows associated with the classical ...

1. Turner RC, Lucke-Wold BP, Hwang R, Underwood BD. Lung cancer metastasis presenting as a solitary skull mass. J Surg Case Rep. 2016;2016(6):rjw116. doi:10.1093/jscr/rjw116 CrossRef Google Scholar

BACKGROUND Motivating adolescents to maintain levels of physical activity (PA) is important because regular PA in adolescence contributes to physical, psychological, and social well-being and PA during adolescence has been associated with activity levels in adulthood. PURPOSE The overall aim of this study is to validate a measure of external reward, health values, and personal interest motiva...

According to a well-known theorem of Cramér and Wold, if P Q are two Borel probability measures on Rd whose projections PL,QL onto each line L in satisfy PL=QL, then P=Q. Our main result is that, both elliptical distributions, then, show that P=Q, it suffices merely check PL=QL for certain set (d2+d)/2 lines L. Moreover optimal. The class distributions contains the Gaussian as well many other m...

The structure of the isometric representations of unital discrete semi-groups with the left cancellation property and no divisors of the identity is studied. We obtain Wold decompositions and prove that the left regular representation of such semigroups is irreducible.

In this paper we consider solutions to the non-stationary Wiener ltering problem using the evolutionary spectral theory. Two cases of interest result from the uncorrelation between the desired signal and the noise. One constrains the support of the generating kernels of the signals and the other imposes orthogonality on their innovation processes. The latter condition is more general and our so...

A free semigroupoid algebra is the weak operator topology closed algebra generated by the left regular representation of a directed graph. We establish lattice isomorphisms between ideals and invariant subspaces, and this leads to a complete description of the wot-closed ideal structure for these algebras. We prove a distance formula to ideals, and this gives an appropriate version of the Carat...