SummaryWe show that smoothness properties of a spectral density matrix and its optimal factor are closely related when the density satisfies theboundedness condition. This is crucial in proving… Expand

A generalized innovation algorithm is used to solve the problems of prediction of future values based on incomplete past and interpolation of missing values of a stationary time series. The emphasis… Expand

Abstract This paper explores a family of weak parallelogram laws for Banach spaces. Some basic properties of such spaces are obtained. The main result is that a Banach space satisfies a lower weak… Expand

Abstract Some geometric properties of Lp spaces are studied which shed light on the prediction of infinite variance processes. In particular, a Pythagorean theorem for Lp is derived. Improved growth… Expand

In Beurling’s approach to inner functions for the shift operator S on the Hardy space H2, a function f is inner when f ⊥ Snf for all \(n \geqslant 1\). Inspired by this approach, this paper develops… Expand

Conditions on cross-generational perturbations of the distribution of male phenotypes that allow for the evolutionary stability of an environmentally canalized threshold are determined.Expand

Let $\Gamma$ be a connected bridgeless graph and fix a vertex $v$ of $\Gamma$. We introduce a bilinear map $\int\colon \mathbf{Z}\pi_1(\Gamma,v) \times T\mathrm{H}_1(\Gamma,\mathbf{Z}) \to… Expand