Related papers: Shift Invariant Spaces on LCA Groups

It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…

Four-dimensional twisted group lattices are used as models for space-time structure. Compared to other attempts at space-time deformation, they have two main advantages: They have a physical interpretation and there is no difficulty in…

A closed subspace is invariant under the Ces\`aro operator $\mathcal{C}$ on the classical Hardy space $H^2(\mathbb D)$ if and only if its orthogonal complement is invariant under the $C_0$-semigroup of composition operators induced by the…

In this work, we consider $\mathbb{Z}^d$-shifts generated by digit substitutions. For such a shift $\mathbb{X}$, we study the elements of the normaliser of $\mathbb{Z}^d$ in the group of self homeomorphisms (called extended symmetries)…

This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…

K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite…

Let $G$ be a compact connected Lie group and $P \to M$ a smooth principal $G$-bundle. Let a `cylinder function' on the space $\A$ of smooth connections on $P$ be a continuous function of the holonomies of $A$ along finitely many piecewise…

We discuss the `hd-compactification' of a semi-simple Lie group to a manifold with corners; it is the real analog of the wonderful compactification of deConcini and Procesi. There is a 1-1 correspondence between the boundary faces of the…

Let $\mathcal{H}$ be Hilbert space and $(\Omega,\mu)$ a $\sigma$-finite measure space. Multiplicatively invariant (MI) spaces are closed subspaces of $ L^2(\Omega, \mathcal{H})$ that are invariant under point-wise multiplication by…

We define local Hardy spaces of differential forms $h^p_{\mathcal D}(\wedge T^*M)$ for all $p\in[1,\infty]$ that are adapted to a class of first order differential operators $\mathcal D$ on a complete Riemannian manifold $M$ with at most…

A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…

Necessary and sufficient conditions are given for density of shift-invariant subspaces of the space $\mathcal{L}$ of integrable functions of bounded support with the inductive limit topology.

The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner…

A bounded function $\phi: G\to \C$ on an LCA group $G$ is called Hartman measurable if it can be extended to a Riemann integrable function $\phi^*: X\to \C$ on some group compactification $(\iota_X,X)$, i.e. on a compact group $X$ such that…

In this article I describe my recent geometric localization argument dealing with actions of NONcompact groups which provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the…

The difference between the quadratic L-groups L_*(A) and the symmetric L-groups L^*(A) of a ring with involution A is detected by generalized Arf invariants. The special case A=Z[x] gives a complete set of invariants for the Cappell…

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…

A theorem of Gerald Schwarz [24, Thm. 1] says that for a linear action of a compact Lie group $G$ on a finite dimensional real vector space $V$ any smooth $G$-invariant function on $V$ can be written as a composite with the Hilbert map. We…

We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…

This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…