Given a Polish topology ? \tau on alttext="script upper B 1 left-parenthesis X right-parenthesis"> <mml:mro...

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator SK on a vector-valued Hardy space H(Ω, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions, and quasi-in...

Light Field Microscopy (LFM) is an imaging technique that captures 3D spatial information with a single 2D image. LFM attractive because of its relatively simple implementation and fast volume acquisition rate. Capturing time series at camera frame rate can enable the study behaviour many biological systems. For instance, it could provide insights into communication dynamics living neural netwo...

We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d dimensional coordinates (where d < D). By a projection to a lower dimensional subspace we obtain a scale invariant non-Gaussian model of Euclidean quantum field theory in D − d or d dimensions.

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator SK on a vector-valued Hardy space H(Ω, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions, and quasi-in...

The purpose of this paper is to introduce and study the notion of a vector-valued π-invariant mean associated to a unitary representation π of a locally compact groupG on S, a self-adjoint linear subspace containing I of B(Hπ). We obtain, among other results, an extension theorem for π-invariant completely positive maps and π-invariant means which characterizes amenability of G. We also study v...

Each normal rational curve Γ in PG(n, F ) admits a group PΓL(Γ) of automorphic collineations. It is well known that for characteristic zero only the empty and the entire subspace are PΓL(Γ)–invariant. In case of characteristic p > 0 there may be further invariant subspaces. For #F ≥ n+ 2, we give a construction of all PΓL(Γ)–invariant subspaces. It turns out that the corresponding lattice is to...